# Triangles

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Right traingles C and D share a leg. If the ratio of the area of traingle C to the area of traingle D is 5:9, C’s hypotenuse is of length 25, and D’s hypotenuse is of length 39, what is the area of C?

• Triangles -

For the non-shared legs,
let the shorter be x and the longer be y

let the length of the shared leg be h
so x^2 + h^2 = 25^2 and y^2 + h^2 = 39^2
h^2 = 625-x^2 and h^2 = 1521 - y^2

625 - x^2 = 1521 - y^2
y^2 - x^2 = 896

Also, (1/2)xh /(1/2)yh = 5/9
x/y = 5/9
9x = 5y
x = 5y/9

y^2 - 25y^2/81 = 896
times 81
81y^2 - 25y^2 = 72576
56y^2 = 72576
y^2 = 1296
y = ± 36 , rejecting the negative, since we can't have a negative length of a line

y= 36, then in x=5y/9 -------->

take it from here

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