Adam B. answered • 07/30/21

A " Young" Professor of Mathematics recently retired

Since we are talking for a right triangle and AB is the longer side , we conclude that AB is the hypotenuse

of the triangle.

So

AC = x

BC = x- 8

AB = x + 8

Then applying the Pythagorean Theorem we have AB^{2} = AC^{2} + BC^{2}

or equivalently ( x + 8 )^{2} = x^{2} + ( x - 8 )^{2}

x^{2} + 16 x + 64 = x^{2} + x^{2} - 16x + 64

32 x = x^{2}

x (32 - x ) = 0

x= 32

Hence AC = 32

BC = 24

AB = 40