Q 8.

Let the sides of a right triangle be $a$ , $b$ , and the hypotenuse $c$ . Then, from the problem statement and the Pythagorean Theorem, respectively:

$\begin{cases} a^2 + b^2 + c^2 = 800 \\ a^2 + b^2 - c^2 = 0 \end{cases}$

Summing the two equations:

$2a^2 + 2b^2 + c^2 - c^2 = 800 + 0$

yields

$a^2 + b^2 = 400$

Substituting this identity into either original equation gives the value of the hypotenuse $c = 20$ .

a^2+b^2+c^2=800 or c^2+c^2=800 or 2c^2=800 or c^2=400 or c=20