Question

DPH is an isosceles right triangle. Determine the missing lengths.

Answer 1

Since DPH is an isosceles right triangle, the legs have the same length, so DH = HP

If the hypotenuse DP is equal √14, we can calculate the legs (x) using Pythagorean Theorem:

$\begin{gathered} DP^2=DH^2+HP^2 \\ (\sqrt[]{14})^2=x^2+x^2 \\ 2x^2=14 \\ x^2=7 \\ x=\sqrt[]{7} \end{gathered}$

So the missing lengths are HP = √7 and DH = √7.