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## Dallasb22 3 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. Dallasb22

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

3. muhammad9t5

find the side and then use use heros formula.

4. muhammad9t5

side c.

5. Dallasb22

You mean to find C?

6. muhammad9t5

yup

7. Dallasb22

So i use: 5√2^2+4√^2=C^2

8. muhammad9t5

by using pythagourus theorm

9. Dallasb22

18=C^2

10. Dallasb22

So i do √18

11. muhammad9t5

thats 3redical2=c

12. muhammad9t5

2sides are in radical then 3rd should be also in radical. do you know radical mean?

13. Dallasb22

Yes the X√x right?

14. muhammad9t5

yes great.

15. Dallasb22

So it would be 9√2^2?

16. muhammad9t5

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

17. Dallasb22

Ok. So C=3√2

18. Dallasb22

What is the Hero's formula?

19. muhammad9t5

therefor c=3redical2

20. Dallasb22

A=5√2, B=4√2, C=3√2

21. muhammad9t5

do you know about Hero's formula ?

22. CliffSedge

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

23. Dallasb22

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

24. CliffSedge

Multiply a×b then divide by 2.

25. Dallasb22

Nice of you to join us, Cliff

26. CliffSedge

*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

5√2 * 4√2= 40 40/2= 20

28. CliffSedge

QED. Good job.

29. muhammad9t5

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

30. Dallasb22

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

31. CliffSedge

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

32. muhammad9t5

ok me too.

33. Dallasb22

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

34. Dallasb22

Thanks Muhammad !

35. Dallasb22

Thanks cliff!

36. Dallasb22

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

37. muhammad9t5

its ok bro. u r welcome.

38. muhammad9t5

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

39. CliffSedge

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

Step 2: Then calculate the Area using:

41. muhammad9t5

means we were dong right or wrong?

42. muhammad9t5

doing

43. muhammad9t5

i was doing without angles.

44. CliffSedge

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

its easy for @Dallasb22

46. muhammad9t5

ok lets see by using herons formula.

47. CliffSedge

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

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

49. Dallasb22

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

50. Dallasb22

Correct?

51. CliffSedge

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

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

53. Dallasb22

Ah true, Cause 1/2BH=Area

54. Dallasb22

I'd still only need base and height.

55. CliffSedge

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

56. CliffSedge

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

57. muhammad9t5

what are the answers of 1st question?

58. Dallasb22

Okay, so 2√3^2+b^2=4^2 6+B^2=16

59. Dallasb22

@muhammad9t5 Answer for Q1 is 20

60. Dallasb22

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

61. Dallasb22

B=√10

62. CliffSedge

mm, something doesn't look right there..

63. Dallasb22

They want my answer to be x√x

64. CliffSedge

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

65. Dallasb22

Ahhhh. Thats my PROBLEM!!!

66. Dallasb22

So it'd be 4√9 = 12

67. Dallasb22

Side B= 2

68. Dallasb22

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

69. Dallasb22

Giving me an area of: 4√3

70. CliffSedge

did you divide by 2?

71. Dallasb22

Ah man. *facepalm*

72. Dallasb22

2√3 IS the area

73. CliffSedge

Math teaches us to be precise and methodical, yes?

74. Dallasb22

Hehe, yes it does.

75. Dallasb22

I have 2 more if you don't mind.

76. Dallasb22

They should be easy, they are equilateral.

77. Dallasb22

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

78. CliffSedge

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

yes.

80. CliffSedge

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

81. Dallasb22

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

82. Dallasb22

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

83. Dallasb22

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

84. Dallasb22

So √3/4 * (25)

85. Dallasb22

I get: 25√3/4

86. Dallasb22

|dw:1347039793370:dw|

87. Dallasb22

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

88. CliffSedge

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

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

90. CliffSedge

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

91. Dallasb22

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

92. Dallasb22

Wait.. I did that wrong.

93. Dallasb22

|dw:1347040273270:dw|

94. Dallasb22

IF the sides are all 5, then AB is 2.5

95. Dallasb22

So how do i put 2.5 into PT?

96. CliffSedge

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

97. CliffSedge

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

98. CliffSedge

I doublechecked. Your original formula and answer were correct.

99. Dallasb22

How could that be?

100. CliffSedge

How could what be?

101. Dallasb22

25√3/4 is the answer?

102. CliffSedge

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

103. Dallasb22

Being 6.25?

104. CliffSedge

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

105. Dallasb22

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

106. CliffSedge

And 6.25√3 is no good?

107. Dallasb22

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

108. Dallasb22

I kept including the 25√3

109. Dallasb22

I included the radical in the the division...

110. Dallasb22

So its 25/4√3 Or 6.25√3

111. Dallasb22

Your Score: 100.0% Thanks Cliff.

112. Dallasb22

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

113. CliffSedge

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

114. Dallasb22

:)

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