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

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1. anonymous

2. anonymous

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

3. anonymous

find the side and then use use heros formula.

4. anonymous

side c.

5. anonymous

You mean to find C?

6. anonymous

yup

7. anonymous

So i use: 5√2^2+4√^2=C^2

8. anonymous

by using pythagourus theorm

9. anonymous

18=C^2

10. anonymous

So i do √18

11. anonymous

thats 3redical2=c

12. anonymous

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

13. anonymous

Yes the X√x right?

14. anonymous

yes great.

15. anonymous

So it would be 9√2^2?

16. anonymous

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

17. anonymous

Ok. So C=3√2

18. anonymous

What is the Hero's formula?

19. anonymous

therefor c=3redical2

20. anonymous

A=5√2, B=4√2, C=3√2

21. anonymous

do you know about Hero's formula ?

22. anonymous

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

23. anonymous

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

24. anonymous

Multiply a×b then divide by 2.

25. anonymous

Nice of you to join us, Cliff

26. anonymous

*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. anonymous

5√2 * 4√2= 40 40/2= 20

28. anonymous

QED. Good job.

29. anonymous

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

30. anonymous

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

31. anonymous

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

32. anonymous

ok me too.

33. anonymous

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

34. anonymous

Thanks Muhammad !

35. anonymous

Thanks cliff!

36. anonymous

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

37. anonymous

its ok bro. u r welcome.

38. anonymous

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

39. anonymous

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. anonymous

Step 2: Then calculate the Area using:

41. anonymous

means we were dong right or wrong?

42. anonymous

doing

43. anonymous

i was doing without angles.

44. anonymous

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. anonymous

its easy for @Dallasb22

46. anonymous

ok lets see by using herons formula.

47. anonymous

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. anonymous

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

49. anonymous

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

50. anonymous

Correct?

51. anonymous

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. anonymous

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

53. anonymous

Ah true, Cause 1/2BH=Area

54. anonymous

I'd still only need base and height.

55. anonymous

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

56. anonymous

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

57. anonymous

what are the answers of 1st question?

58. anonymous

Okay, so 2√3^2+b^2=4^2 6+B^2=16

59. anonymous

@muhammad9t5 Answer for Q1 is 20

60. anonymous

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

61. anonymous

B=√10

62. anonymous

mm, something doesn't look right there..

63. anonymous

They want my answer to be x√x

64. anonymous

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

65. anonymous

Ahhhh. Thats my PROBLEM!!!

66. anonymous

So it'd be 4√9 = 12

67. anonymous

Side B= 2

68. anonymous

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

69. anonymous

Giving me an area of: 4√3

70. anonymous

did you divide by 2?

71. anonymous

Ah man. *facepalm*

72. anonymous

2√3 IS the area

73. anonymous

Math teaches us to be precise and methodical, yes?

74. anonymous

Hehe, yes it does.

75. anonymous

I have 2 more if you don't mind.

76. anonymous

They should be easy, they are equilateral.

77. anonymous

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

78. anonymous

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. anonymous

yes.

80. anonymous

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

81. anonymous

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

82. anonymous

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

83. anonymous

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

84. anonymous

So √3/4 * (25)

85. anonymous

I get: 25√3/4

86. anonymous

|dw:1347039793370:dw|

87. anonymous

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

88. anonymous

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. anonymous

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

90. anonymous

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

91. anonymous

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

92. anonymous

Wait.. I did that wrong.

93. anonymous

|dw:1347040273270:dw|

94. anonymous

IF the sides are all 5, then AB is 2.5

95. anonymous

So how do i put 2.5 into PT?

96. anonymous

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

97. anonymous

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

98. anonymous

I doublechecked. Your original formula and answer were correct.

99. anonymous

How could that be?

100. anonymous

How could what be?

101. anonymous

25√3/4 is the answer?

102. anonymous

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

103. anonymous

Being 6.25?

104. anonymous

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

105. anonymous

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

106. anonymous

And 6.25√3 is no good?

107. anonymous

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

108. anonymous

I kept including the 25√3

109. anonymous

I included the radical in the the division...

110. anonymous

So its 25/4√3 Or 6.25√3

111. anonymous

Your Score: 100.0% Thanks Cliff.

112. anonymous

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

113. anonymous

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

114. anonymous

:)

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