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The perimeter of a right triangle is 24cm. If the hypotenuse is 10cm , find the other two sides.?
The perimeter of a right triangle is 24cm. If the hypotenuse is 10cm , find the other two sides.? Let x and y be the other two sides of the right triangle, We were given: x + y = 24 - 10 = 14; y = 14 - x (equation 1) x^2 + y^2 = 10^2 = 100 (equation 2) Replace y in the equation 2 we have: x^2 + ( 14 - x)^2 = 100 x^2 + 196 - 28x + x^2 = 100 2x^2 - 28x + 96 = 0 x^2 - 14x + 48 = 0 (x - 6)(x - 8) = 0 x = 6 or x = 8 y = 14 - 6 = 8 or y = 14 - 8 = 6 The other two sides are 6cm and 8cm respectively.
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Asked 4/22/2014 9:50:56 AM
Updated 4/22/2014 11:55:42 PM
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The perimeter of a right triangle is 24cm. If the hypotenuse is 10cm , find the other two sides.?
Let x and y be the other two sides of the right triangle,
We were given:
x + y = 24 - 10 = 14; y = 14 - x (equation 1)
x^2 + y^2 = 10^2 = 100 (equation 2)
Replace y in the equation 2 we have:
x^2 + ( 14 - x)^2 = 100
x^2 + 196 - 28x + x^2 = 100
2x^2 - 28x + 96 = 0
x^2 - 14x + 48 = 0
(x - 6)(x - 8) = 0
x = 6 or x = 8
y = 14 - 6 = 8 or y = 14 - 8 = 6
The other two sides are 6cm and 8cm respectively.
Added 4/22/2014 11:55:42 PM
This answer has been confirmed as correct and helpful.
Confirmed by jeifunk [4/23/2014 12:07:07 AM]
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