Question

Find the value of y and simplify completely

Answer 1

Here we have three similar triangles

In similar triangles sides are in proportion

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.

`(part of hypotenuse )/(altitude) =(altitude)/(other part of hypotenuse)`

`(16)/(y) =(y)/(4)`

We cross multiply to solve for y

`y^(2) =64`

Taking root of both sides

y=8