Answer:
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
