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.

$\frac{part of hypotenuse }{altitude} =\frac{altitude}{other part of hypotenuse}$

$\frac{16}{y} =\frac{y}{4}$

We cross multiply to solve for y

$y^{2} =64$

Taking root of both sides

y=8