Question

What is the measure of z?

16
y
X
z = 4√ [?]
Give your answer in simplest form.

Answer 1

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.

`\cfrac{z}{20}=\cfrac{4}{z}\implies z^2=4(20)\implies z^2=4(4\cdot 5)\implies z^2=4^2\cdot 5 \\\\\\ z=√(4^2\cdot 5)\implies z=4√(5)`