SOLUTION: The hypotenuse of a right triangle is 13 inches. Find the perimeter of this triangle if its area is 30 square inches.

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Question 726747: The hypotenuse of a right triangle is 13 inches. Find the perimeter of this triangle if its area is 30 square inches.
Answer by wfalbino(2) About Me  (Show Source):
You can put this solution on YOUR website!
using pythagorean, a%5E2%2Bb%5E2=h%5E2
a%5E2%2Bb%5E2=13%5E2
a%5E2%2Bb%5E2=169_in%5E2 --> equation 1
area of your triangle is A=%281%2F2%29%28ab%29
30=%281%2F2%29%28ab%29
60_in%5E2=ab --> equation 2

perimeter is P=a%2Bb%2Bh
solve for a+b

square a+b=%28a%2Bb%29%5E2
a%5E2%2B2ab%2Bb%5E2=%28a%5E2%2Bb%5E2%29%2B2ab---> equation 3

substitute eq 1 and eq 2 to eq3
%28a%5E2%2Bb%5E2%29%2B2ab=169%2B%282%2A60%29

your %28a%2Bb%29%5E2 is now equal to 289
%28a%2Bb%29=sqrt%28289_in%5E2%29=17_in

recall P=a%2Bb%2Bh
P=17%2B13=30_in

hope it helps =)