# Geometrey

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A right triangle has perimeter equal to 80 and hypotenuse equal to 34. What is the area of the triangle?

• Geometrey -

let one leg be x
then the other leg is 80 - 34 - x = 46-x

x^2 + (46-x)^2 = 34^2
x^2 + 2116 - 92x + x^2 = 1156
2x^2 - 92x + 960 = 0
x^2 - 46x + 480 = 0
(x -30)(x-16) = 0
x = 30 or x = 16
if x=30, other leg is 46-30 = 16
if x = 16 , then other leg is 46-16 = 30
(symmetrical solution)

area of triangle = (1/2)(16)(30) = 240 square units

• Geometrey -

Thanks! :)

I thought it made sense to make it into a quadratic equation.

Stupid me... I didn't factorise correctly.

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