Question

find the square of the hypotenuse of a right triangle with a and b related by the statement a=b-5

Answer 1

The hypotenuse is given by the Pythagorean theorem:

$c=\sqrt{a^2+b^2}$

Since a=b-5, the expression becomes

$c=\sqrt{(b-5)^2+b^2}$

Expand the square

$c=\sqrt{b^2-10b+25+b^2}=\sqrt{2b^2-10b+25}$

Unless you're given an explicit value for b, that's all we can say.