Question

The perimeter of XYZ is ___ units.

Answer 1

Look at the picture.

$ZY = 5+3=8$

For XY and ZX use the Pythagorean theorem.

$XY^2=3^2+4^2\\\\XY^2=9+16\\\\XY^2=25\to XY=\sqrt{25}\\\\XY=5$

$ZX^2=5^2+4^2\\\\ZX^2=25+16\\\\ZX^2=41\to ZX=\sqrt{41}$

The perimetero fo XYZ:

$P_{\triangle XYZ}=8+5+\sqrt{41}=\boxed{13+\sqrt{41}}$