Question

Solve for z (attachment)

Answer 1

Look at the picture.

`\Delta ABD\ and\ \Delta BCD\ are\ similar,\ therefore:\\\\(y)/(4)=(16)/(y)\ \ \ \ |cross\ multiply\\\\y\cdot y=4\cdot16\\\\y^2=64\to y=√(64)\to y=8`
Use Pythagorean theory:

`z^2=4^2+8^2\\\\z^2=16+64\\\\z^2=80\to z=√(80)\\\\z=√(16\cdot5)\\\\z=√(16)\cdot\sqrt5\\\\\boxed{z=4\sqrt5}`

Answer 2

By similar triangles
z / 4 = (16 + 4)/z
z^2 / 4 = 20
z^2 = 80
z = 4√5
Therefore the answer to this question is z = 4√5.