WXYZ is a square of side length 30. V is a point on XY and P is a point inside the square with PV $\perp$   XY. If PW $=$  PZ $=$  PV – 5, then PV is

Given that

$PW=PZ=PV-5$

$PW=x$

$\therefore PV=x+5$

$\therefore PM=30-PV\left(\text{Draw PM}\perp \text{WZ}\right)$

$=25-x$

$\Delta PMW,$

$x^2=P{M}^2+M{W}^2$

$x^2={\left(25-x\right)}^2+{15}^2$

$\Rightarrow x=17$

$\therefore PV=x+5=17+5=22$