The longer leg of a right triangle is 4 more than the short leg. The hypotenuse is eight less than the sum of the 2 legs. Solve

SteLet a = short leg of the right triangle, b = the longer leg, and c = the hypotenuse.

The longer leg of a right triangle is 4inches longer than the shorter leg: b = a + 4

The hypotenuse is 8inches longer than the shorter leg:  c = a + 8

Use the Pythagorean Theorem:

a2 + b2 = c2

a2 + (a+4)2 = (a+8)2

a2 + a2 + 8a + 16 = a2 + 16a + 64

a2 - 8a - 48 = 0

Factors to:

(a-12)(a+4) = 0

a = 12, -4

Since we can't have a side of -4, a = 12

Shorter Leg = 12 inches

Longer Leg = 12 + 4 = 16 inches

Hypotenuse = 12 + 8 = 20 inches