1 Answer

Nmjk · Answer 1 · 2019-11-07T13:24:59+0000

In the smaller triangle, let
be the length of the smallest leg. Then the smallest leg in the larger triangle is
14-y .

Within the scope of the smaller triangle, we have
such that

$x^2+y^2=13^2\implies y=√(13^2-x^2)$

Then within the larger the triangle, we would have

$x^2+(14-y)^2=15^2\iff x^2+\left(14-√(13^2-x^2)\right)^2=15^2$

Now we can solve for
:

x^2+14^2-28√(13^2-x^2)+(13^2-x^2)=15^2

$\implies x=12$

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