Question

The shorter leg of a right triangle is 8 less than the hypotenuse. The longer leg is 1 less than the hypotenuse. Find the perimeter of the triangle.

Answer 1

Perimeter is 30

Step-by-step explanation:

short leg = h - 8

longer leg = h -1

(h-8)^2 + (h -1)^2 = h^2

h^2 - 16h + 64 + h^2 - 2h + 1 = h^2

h^2 - 16h + 64 + h^2 - 2h + 1 - h^2 = 0

h^2 - 18h + 65 = 0

(h - 13 )(h - 5 ) = 0

h-13 = 0 ---> h = 13 ---> short leg is 5 and long leg is 12 ---> perimeter is 30

h-5 = 0 ---> h = 5 --> short leg is -3 and long leg is 4 <--- disqualified because leg measure cannot be negative

short leg is 5, long leg is 12, hypotneuse is 13

5^2 + 12^2 = 25 + 144 = 169 = 13^2 <--- pythagorean check

perimeter is 5 + 12 + 13 = 30