## Dallasb22 Group Title What is the area of a right triangle with Side a: 5√2 Side b: 4√2? one year ago one year ago

1. Dallasb22 Group Title

2. Dallasb22 Group Title

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

find the side and then use use heros formula.

side c.

5. Dallasb22 Group Title

You mean to find C?

yup

7. Dallasb22 Group Title

So i use: 5√2^2+4√^2=C^2

by using pythagourus theorm

9. Dallasb22 Group Title

18=C^2

10. Dallasb22 Group Title

So i do √18

thats 3redical2=c

13. Dallasb22 Group Title

Yes the X√x right?

yes great.

15. Dallasb22 Group Title

So it would be 9√2^2?

$18=\sqrt{3*3*2}$ $18=\sqrt{9*2}$ u know the square roof of 9 is 3 then $18=3\sqrt{2}$

17. Dallasb22 Group Title

Ok. So C=3√2

18. Dallasb22 Group Title

What is the Hero's formula?

therefor c=3redical2

20. Dallasb22 Group Title

A=5√2, B=4√2, C=3√2

do you know about Hero's formula ?

22. CliffSedge Group Title

If it's a right triangle, you don't need Heron's formula . . .

23. Dallasb22 Group Title

I don't know Heron's formula. And yes, it is a Right Triangle

24. CliffSedge Group Title

Multiply a×b then divide by 2.

25. Dallasb22 Group Title

26. CliffSedge Group Title

*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 Group Title

5√2 * 4√2= 40 40/2= 20

28. CliffSedge Group Title

QED. Good job.

yes i am in that i am talking about Hero's formula not herons.

30. Dallasb22 Group Title

Okay, good to know, i googled Heron's formula. Hero formula=Heron's formula

31. CliffSedge Group Title

Same guy. Heron is another name for Hero of Alexandria (en.wikipedia.org/wiki/Hero_of_Alexandria)

ok me too.

33. Dallasb22 Group Title

I also, noted down Heron's formula for later use :D So the area: 20?

34. Dallasb22 Group Title

35. Dallasb22 Group Title

Thanks cliff!

36. Dallasb22 Group Title

I have another question if one of you don't mind

its ok bro. u r welcome.

bro look at here what is says http://www.mathsisfun.com/geometry/herons-formula.html

39. CliffSedge Group Title

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.

Step 2: Then calculate the Area using:

means we were dong right or wrong?

doing

i was doing without angles.

44. CliffSedge Group Title

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.

its easy for @Dallasb22

ok lets see by using herons formula.

47. CliffSedge Group Title

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 Group Title

Be my guest. Heron's formula is a beast and not worth my time.

49. Dallasb22 Group Title

Yes, receiving the third side is only necessary if we use Heron's formula.

50. Dallasb22 Group Title

Correct?

51. CliffSedge Group Title

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 Group Title

@CliffSedge Another right triangle, A=2√3 c=4 What do i do here?

53. Dallasb22 Group Title

Ah true, Cause 1/2BH=Area

54. Dallasb22 Group Title

I'd still only need base and height.

55. CliffSedge Group Title

If you now have a leg and the hypotenuse, use PT to find the other leg then same as before.

56. CliffSedge Group Title

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

what are the answers of 1st question?

58. Dallasb22 Group Title

Okay, so 2√3^2+b^2=4^2 6+B^2=16

59. Dallasb22 Group Title

60. Dallasb22 Group Title

So i subtract 6 to both sides B^2=10

61. Dallasb22 Group Title

B=√10

62. CliffSedge Group Title

mm, something doesn't look right there..

63. Dallasb22 Group Title

They want my answer to be x√x

64. CliffSedge Group Title

I think you forgot to square the 2 in (2√3)

65. Dallasb22 Group Title

Ahhhh. Thats my PROBLEM!!!

66. Dallasb22 Group Title

So it'd be 4√9 = 12

67. Dallasb22 Group Title

Side B= 2

68. Dallasb22 Group Title

So I would multiply A and B 2√3 * 2 =X x/2=Area?

69. Dallasb22 Group Title

Giving me an area of: 4√3

70. CliffSedge Group Title

did you divide by 2?

71. Dallasb22 Group Title

Ah man. *facepalm*

72. Dallasb22 Group Title

2√3 IS the area

73. CliffSedge Group Title

Math teaches us to be precise and methodical, yes?

74. Dallasb22 Group Title

Hehe, yes it does.

75. Dallasb22 Group Title

I have 2 more if you don't mind.

76. Dallasb22 Group Title

They should be easy, they are equilateral.

77. Dallasb22 Group Title

I just am doing something wrong that I can't find..

78. CliffSedge Group Title

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.

yes.

80. CliffSedge Group Title

Wanna take this equilateral triangle, muhammad? I'm going to take a coffee break.

81. Dallasb22 Group Title

Yes, i know what you mean. If you didn't catch me I would have gotten it wrong, because I was rushing.

82. Dallasb22 Group Title

All three sides: 5, so the perimeter: 15 What is the area?

83. Dallasb22 Group Title

Equilateral triangle area formula: √3/4 * (s^2)

84. Dallasb22 Group Title

So √3/4 * (25)

85. Dallasb22 Group Title

I get: 25√3/4

86. Dallasb22 Group Title

|dw:1347039793370:dw|

87. Dallasb22 Group Title

But i cannot insert that in my work, i can only enter x√x

88. CliffSedge Group Title

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 Group Title

But what use is PT, if all side's are equal?

90. CliffSedge Group Title

To solve for the height of the triangle, which you need for the general triangle area formula.

91. Dallasb22 Group Title

Okay.. So the height is 25? 25+25=25 50=25 25

92. Dallasb22 Group Title

Wait.. I did that wrong.

93. Dallasb22 Group Title

|dw:1347040273270:dw|

94. Dallasb22 Group Title

IF the sides are all 5, then AB is 2.5

95. Dallasb22 Group Title

So how do i put 2.5 into PT?

96. CliffSedge Group Title

|dw:1347040269678:dw| $(S/2)^2+h^2=S^2 \rightarrow h^2=S^2-S^2/4 = 3S^2/4$

97. CliffSedge Group Title

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

98. CliffSedge Group Title

99. Dallasb22 Group Title

How could that be?

100. CliffSedge Group Title

How could what be?

101. Dallasb22 Group Title

102. CliffSedge Group Title

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

103. Dallasb22 Group Title

Being 6.25?

104. CliffSedge Group Title

Yes. 2.5^2 = 6.25 just like 25^2 = 625.

105. Dallasb22 Group Title

But wait.. Something is wrong, because they want my answer as: x√x

106. CliffSedge Group Title

And 6.25√3 is no good?

107. Dallasb22 Group Title

Darn, there i go again I forgot we were only simplifying the 25/4

108. Dallasb22 Group Title

I kept including the 25√3

109. Dallasb22 Group Title

I included the radical in the the division...

110. Dallasb22 Group Title

So its 25/4√3 Or 6.25√3

111. Dallasb22 Group Title

112. Dallasb22 Group Title

Those 2 were the only ones I was having trouble with.

113. CliffSedge Group Title

My pleasure. They're all just puzzles. Keep looking until you find where all the pieces fit.

114. Dallasb22 Group Title

:)