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.

Perimeter is 30

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