SOLUTION: In a right triangle one leg is 9 cm less than the hypotenuse. The other leg is 2 cm less than the hypotenuse. How do I find the length of each side?

Algebra ->  Pythagorean-theorem -> SOLUTION: In a right triangle one leg is 9 cm less than the hypotenuse. The other leg is 2 cm less than the hypotenuse. How do I find the length of each side?      Log On


   

Question 366930: In a right triangle one leg is 9 cm less than the hypotenuse. The other leg is 2 cm less than the hypotenuse. How do I find the length of each side?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since it's a right triangle, it obeys the Pythagorean theorem,
a%5E2%2Bb%5E2=h%5E2
%28h-9%29%5E2%2B%28h-2%29%5E2=h%5E2
h%5E2-18h%2B81%2Bh%5E2-4h%2B4=h%5E2
h%5E2-22h%2B85=0
%28h-7%29%28h-15%29=0
Two solutions:
h=7
Then a=7-9
This is not a possible solution since it leads to a negative length.
.
.
.
h-15=0
highlight%28h=15%29cm
.
.
a=15-9
highlight%28a=6%29cm
.
.
b=15-2
highlight%28b=13%29cm