Question

If e= 144 and f=25, solve for lengths a, b, c, and d. picture in comments.

Answer 1

Use \[a^2 + b^2 = c^2\]

Answer 2

That should help you

Answer 3

The big right triangle with sides a,b and c is divided into two smaller right triangles.
*All three triangles are similar*
That means you can write ratios of "corresponding sides"
the short leg to long leg of the left triangle is d/e
and the short leg to long leg of the right triangle is f/d
because the triangles are similar you can say
\[ \frac{d}{e} = \frac{f}{d} \]
They tell you e= 144 and f=25
so

\[ \frac{d}{144} = \frac{25}{d} \]
cross multiply and solve for d