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Dallasb22

  • 2 years ago

What is the area of a right triangle with Side a: 5√2 Side b: 4√2?

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  1. Dallasb22
    • 2 years ago
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  2. Dallasb22
    • 2 years ago
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    I got 10.. Formula to find right angle: A=1/2BH

  3. muhammad9t5
    • 2 years ago
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    find the side and then use use heros formula.

  4. muhammad9t5
    • 2 years ago
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    side c.

  5. Dallasb22
    • 2 years ago
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    You mean to find C?

  6. muhammad9t5
    • 2 years ago
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    yup

  7. Dallasb22
    • 2 years ago
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    So i use: 5√2^2+4√^2=C^2

  8. muhammad9t5
    • 2 years ago
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    by using pythagourus theorm

  9. Dallasb22
    • 2 years ago
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    18=C^2

  10. Dallasb22
    • 2 years ago
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    So i do √18

  11. muhammad9t5
    • 2 years ago
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    thats 3redical2=c

  12. muhammad9t5
    • 2 years ago
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    2sides are in radical then 3rd should be also in radical. do you know radical mean?

  13. Dallasb22
    • 2 years ago
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    Yes the X√x right?

  14. muhammad9t5
    • 2 years ago
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    yes great.

  15. Dallasb22
    • 2 years ago
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    So it would be 9√2^2?

  16. muhammad9t5
    • 2 years ago
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    \[18=\sqrt{3*3*2}\] \[18=\sqrt{9*2}\] u know the square roof of 9 is 3 then \[18=3\sqrt{2}\]

  17. Dallasb22
    • 2 years ago
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    Ok. So C=3√2

  18. Dallasb22
    • 2 years ago
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    What is the Hero's formula?

  19. muhammad9t5
    • 2 years ago
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    therefor c=3redical2

  20. Dallasb22
    • 2 years ago
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    A=5√2, B=4√2, C=3√2

  21. muhammad9t5
    • 2 years ago
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    do you know about Hero's formula ?

  22. CliffSedge
    • 2 years ago
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    If it's a right triangle, you don't need Heron's formula . . .

  23. Dallasb22
    • 2 years ago
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    I don't know Heron's formula. And yes, it is a Right Triangle

  24. CliffSedge
    • 2 years ago
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    Multiply a×b then divide by 2.

  25. Dallasb22
    • 2 years ago
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    Nice of you to join us, Cliff

  26. CliffSedge
    • 2 years ago
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    *salutes* Heron's formula is general for any kind of triangle where you don't feel like using trigonometry to find the height. It requires that you know all three sides first, so often, you'll need trigonometry anyway.

  27. Dallasb22
    • 2 years ago
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    5√2 * 4√2= 40 40/2= 20

  28. CliffSedge
    • 2 years ago
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    QED. Good job.

  29. muhammad9t5
    • 2 years ago
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    yes i am in that i am talking about Hero's formula not herons.

  30. Dallasb22
    • 2 years ago
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    Okay, good to know, i googled Heron's formula. Hero formula=Heron's formula

  31. CliffSedge
    • 2 years ago
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    Same guy. Heron is another name for Hero of Alexandria (en.wikipedia.org/wiki/Hero_of_Alexandria)

  32. muhammad9t5
    • 2 years ago
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    ok me too.

  33. Dallasb22
    • 2 years ago
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    I also, noted down Heron's formula for later use :D So the area: 20?

  34. Dallasb22
    • 2 years ago
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    Thanks Muhammad !

  35. Dallasb22
    • 2 years ago
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    Thanks cliff!

  36. Dallasb22
    • 2 years ago
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    I have another question if one of you don't mind

  37. muhammad9t5
    • 2 years ago
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    its ok bro. u r welcome.

  38. muhammad9t5
    • 2 years ago
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    bro look at here what is says http://www.mathsisfun.com/geometry/herons-formula.html

  39. CliffSedge
    • 2 years ago
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    Heron's formula is pretty cool, but I prefer using the Law of Sines and Law of Cosines better (provided you know at least 1 angle.

  40. muhammad9t5
    • 2 years ago
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    Step 2: Then calculate the Area using:

  41. muhammad9t5
    • 2 years ago
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    means we were dong right or wrong?

  42. muhammad9t5
    • 2 years ago
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    doing

  43. muhammad9t5
    • 2 years ago
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    i was doing without angles.

  44. CliffSedge
    • 2 years ago
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    Area of any triangle is half the product of the base and height. For a right triangle, the two perpendicular legs are the base and height.

  45. muhammad9t5
    • 2 years ago
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    its easy for @Dallasb22

  46. muhammad9t5
    • 2 years ago
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    ok lets see by using herons formula.

  47. CliffSedge
    • 2 years ago
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    Actually, you were doing it with angles because you saw the right angle and used Pythagoras' theorem for the third side (which was unnecessary).

  48. CliffSedge
    • 2 years ago
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    Be my guest. Heron's formula is a beast and not worth my time.

  49. Dallasb22
    • 2 years ago
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    Yes, receiving the third side is only necessary if we use Heron's formula.

  50. Dallasb22
    • 2 years ago
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    Correct?

  51. CliffSedge
    • 2 years ago
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    and if it wasn't a right angle, then you'd have to use law of cosines or law of sines to find the third side, and if you're going to use trig anyway, might as well solve for the height instead (which is easier) and you still don't need Heron's formula.

  52. Dallasb22
    • 2 years ago
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    @CliffSedge Another right triangle, A=2√3 c=4 What do i do here?

  53. Dallasb22
    • 2 years ago
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    Ah true, Cause 1/2BH=Area

  54. Dallasb22
    • 2 years ago
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    I'd still only need base and height.

  55. CliffSedge
    • 2 years ago
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    If you now have a leg and the hypotenuse, use PT to find the other leg then same as before.

  56. CliffSedge
    • 2 years ago
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    As a fun exercise just to practice some arithmetic, you can use Heron's formula to verify the area, or vice-verse.

  57. muhammad9t5
    • 2 years ago
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    what are the answers of 1st question?

  58. Dallasb22
    • 2 years ago
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    Okay, so 2√3^2+b^2=4^2 6+B^2=16

  59. Dallasb22
    • 2 years ago
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    @muhammad9t5 Answer for Q1 is 20

  60. Dallasb22
    • 2 years ago
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    So i subtract 6 to both sides B^2=10

  61. Dallasb22
    • 2 years ago
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    B=√10

  62. CliffSedge
    • 2 years ago
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    mm, something doesn't look right there..

  63. Dallasb22
    • 2 years ago
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    They want my answer to be x√x

  64. CliffSedge
    • 2 years ago
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    I think you forgot to square the 2 in (2√3)

  65. Dallasb22
    • 2 years ago
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    Ahhhh. Thats my PROBLEM!!!

  66. Dallasb22
    • 2 years ago
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    So it'd be 4√9 = 12

  67. Dallasb22
    • 2 years ago
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    Side B= 2

  68. Dallasb22
    • 2 years ago
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    So I would multiply A and B 2√3 * 2 =X x/2=Area?

  69. Dallasb22
    • 2 years ago
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    Giving me an area of: 4√3

  70. CliffSedge
    • 2 years ago
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    did you divide by 2?

  71. Dallasb22
    • 2 years ago
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    Ah man. *facepalm*

  72. Dallasb22
    • 2 years ago
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    2√3 IS the area

  73. CliffSedge
    • 2 years ago
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    Math teaches us to be precise and methodical, yes?

  74. Dallasb22
    • 2 years ago
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    Hehe, yes it does.

  75. Dallasb22
    • 2 years ago
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    I have 2 more if you don't mind.

  76. Dallasb22
    • 2 years ago
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    They should be easy, they are equilateral.

  77. Dallasb22
    • 2 years ago
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    I just am doing something wrong that I can't find..

  78. CliffSedge
    • 2 years ago
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    And remember, that is more important than any particular kind of math problem. It's the problem-solving attitude, the patience, the planning, that is more important than whether or not you can solve this or that equation.

  79. muhammad9t5
    • 2 years ago
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    yes.

  80. CliffSedge
    • 2 years ago
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    Wanna take this equilateral triangle, muhammad? I'm going to take a coffee break.

  81. Dallasb22
    • 2 years ago
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    Yes, i know what you mean. If you didn't catch me I would have gotten it wrong, because I was rushing.

  82. Dallasb22
    • 2 years ago
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    All three sides: 5, so the perimeter: 15 What is the area?

  83. Dallasb22
    • 2 years ago
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    Equilateral triangle area formula: √3/4 * (s^2)

  84. Dallasb22
    • 2 years ago
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    So √3/4 * (25)

  85. Dallasb22
    • 2 years ago
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    I get: 25√3/4

  86. Dallasb22
    • 2 years ago
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    |dw:1347039793370:dw|

  87. Dallasb22
    • 2 years ago
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    But i cannot insert that in my work, i can only enter x√x

  88. CliffSedge
    • 2 years ago
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    hmm, I'm getting something different. I'm going to doublecheck my work. In the meantime, if you forget the equilateral triangle formula, you can rederive it using (what else?) Pythagoras' theorem. |dw:1347039924563:dw|

  89. Dallasb22
    • 2 years ago
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    But what use is PT, if all side's are equal?

  90. CliffSedge
    • 2 years ago
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    To solve for the height of the triangle, which you need for the general triangle area formula.

  91. Dallasb22
    • 2 years ago
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    Okay.. So the height is 25? 25+25=25 50=25 25

  92. Dallasb22
    • 2 years ago
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    Wait.. I did that wrong.

  93. Dallasb22
    • 2 years ago
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    |dw:1347040273270:dw|

  94. Dallasb22
    • 2 years ago
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    IF the sides are all 5, then AB is 2.5

  95. Dallasb22
    • 2 years ago
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    So how do i put 2.5 into PT?

  96. CliffSedge
    • 2 years ago
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    |dw:1347040269678:dw| \[(S/2)^2+h^2=S^2 \rightarrow h^2=S^2-S^2/4 = 3S^2/4\]

  97. CliffSedge
    • 2 years ago
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    Half of 5 is (5/2). (5/2)^2 = 25/4. (tip: fractions are better than decimals when doing algebra)

  98. CliffSedge
    • 2 years ago
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    I doublechecked. Your original formula and answer were correct.

  99. Dallasb22
    • 2 years ago
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    How could that be?

  100. CliffSedge
    • 2 years ago
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    How could what be?

  101. Dallasb22
    • 2 years ago
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    25√3/4 is the answer?

  102. CliffSedge
    • 2 years ago
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    Yep. If wherever you are submitting these answers doesn't like it in fraction form, then convert 25/4 into a decimal.

  103. Dallasb22
    • 2 years ago
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    Being 6.25?

  104. CliffSedge
    • 2 years ago
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    Yes. 2.5^2 = 6.25 just like 25^2 = 625.

  105. Dallasb22
    • 2 years ago
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    But wait.. Something is wrong, because they want my answer as: x√x

  106. CliffSedge
    • 2 years ago
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    And 6.25√3 is no good?

  107. Dallasb22
    • 2 years ago
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    Darn, there i go again I forgot we were only simplifying the 25/4

  108. Dallasb22
    • 2 years ago
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    I kept including the 25√3

  109. Dallasb22
    • 2 years ago
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    I included the radical in the the division...

  110. Dallasb22
    • 2 years ago
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    So its 25/4√3 Or 6.25√3

  111. Dallasb22
    • 2 years ago
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    Your Score: 100.0% Thanks Cliff.

  112. Dallasb22
    • 2 years ago
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    Those 2 were the only ones I was having trouble with.

  113. CliffSedge
    • 2 years ago
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    My pleasure. They're all just puzzles. Keep looking until you find where all the pieces fit.

  114. Dallasb22
    • 2 years ago
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    :)

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