The shorter leg of a right triangle is 8 inches shorter than the longer leg. The hypotenuse is 8 inches longer than the longer leg. Find the

Let  L  represent the length of the longer leg.

Then  L - 8  represents the length of the shorter leg and  L + 8  represents the length of the longer leg.

Using the Pythagorean theorem:  (L)² + (L - 8)²  =  (L + 8)²

Multiplying out:                         L²  + L² - 16L + 64  =  L² + 16L + 64

Subtract 64 from both sides:      L²  + L² - 16L  =  L² + 16L

Subtract L² from both sides:      L² - 16L  =  16L

Subtract 16L from both sides:    L² - 32L  =  0

Factor:                                     L(L - 32)  =  0

Either     L = 0  (impossible)     or     L - 32  = 0     --->     L  =  32

If  L = 32,  then  L - 8  = 24     and     L + 8 = 40 

The longer leg of a right tnangle is 4 inches longer than the shorter leg. The hypotenuse is 8 inches longer than the shorter leg. Find the side lengths of the triangle.