Question

Geometry question (file upload)

Answer 1

Look at the picture.

`\Delta ADC\ and\ \Delta CDB\ are\ similar\ therefore\\\\(y)/(4)=(9)/(y)\ \ \ \ |cross\ multiply\\\\y\cdot y=4\cdot9\\\\y^2=36\to y=√(36)\to y=6`
Use Pythagorean theorem.

`z^2=6^2+9^2\\\\z^2=36+81\\\\z^2=117\\\\z=√(117)\\\\z=√(9\cdot13)\\\\z=\sqrt9\cdot√(13)\\\\\boxed{z=3√(13)}`