Question

One leg of triangle is 7 inches longer than the other leg. The hypotenuse is 8 inches longer than the shorter leg. The perimeter of the triangle is

Answer 1

Answer:

5 ; 12 ; 13

Step-by-step explanation:

Let :

Shorter leg = x

Other leg = x + 7

Hypotenus = x + 8

Recall:

Hypotenus² = opposite² + adjacent²

(x+8)² = x² + (x+7)²

x² + 16x + 64 = x² + x² + 14x + 49

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

x(x - 5) +3(x - 5) = 0

(x + 3) = 0 ; x = - 3

(x - 5) = 0 ; x = 5

Side can't be negative ;

Hence,

x = shorter side = 5

Other side = x + 7 = 5 + 7 = 12

Hypotenus = x + 8 = 5 + 8 = 13