SOLUTION: Not understanding how to solve this type of problem... In a right triangle one side is 1 unit longer than the other side and the perimeter is 12 feet. Find the length of the hyp

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: Not understanding how to solve this type of problem... In a right triangle one side is 1 unit longer than the other side and the perimeter is 12 feet. Find the length of the hyp      Log On


   

Question 168699: Not understanding how to solve this type of problem...
In a right triangle one side is 1 unit longer than the other side and the perimeter is 12 feet. Find the length of the hypotenuse.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call x the hypothenuse and sides a, a+1(because one side is one unit longer)
:
we know thata%5E2%2B%28a%2B1%29%5E2=x%5E2 but we also know that P=a+a+1+x::: 12=2a+1+x
:
x=11-2a----. plug this value into the 1st equation.
:
a%5E2%2B%28a%2B1%29%5E2=%2811-2a%29%5E2 solve for a
a%5E2%2Ba%5E2%2B2a%2B1=121-44a%2B4a%5E2
:
2a%5E2-46a%2B120=0 divide by 2
:
a%5E2-23a%2B60=0 factor
:
%28a-20%29%28a-3%29=0
:
highlight%28a=20%29 highlight%28a=3%29
x=11-2a....11-2(20)=-29 so throw that out as its a negative length
...........11-2(3)=5
so one side is 3 the other side is 4 and the hypothenuse is 5