SOLUTION: The length of the longer leg of a right triangle is 13m more than three times the length of the shorter leg. The length of the hypotenuse is 14m more than three times the length of

Algebra ->  Pythagorean-theorem -> SOLUTION: The length of the longer leg of a right triangle is 13m more than three times the length of the shorter leg. The length of the hypotenuse is 14m more than three times the length of      Log On


   

Question 957229: The length of the longer leg of a right triangle is 13m more than three times the length of the shorter leg. The length of the hypotenuse is 14m more than three times the length of the shorter leg. Find the side lengths of the triangle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
L=13%2B3S
H=14%2B3S
S%5E2%2BL%5E2=H%5E2
S%5E2%2B%2813%2B3S%29%5E2=%2814%2B3S%29%5E2
S%5E2%2B9S%5E2%2B78S%2B169=9S%5E2%2B84S%2B196
10S%5E2%2B78S%2B169=9S%5E2%2B84S%2B196
S%5E2-6S-27=0
%28S-9%29%28S%2B3%29=0
Two solution but only one is positive,
S-9=0
S=9
Then,
L=13%2B3%289%29
L=13%2B27
L=40
and
H=14%2B27
H=41