SOLUTION: Hello! I need help solving the following please...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.

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Question 56484: Hello! I need help solving the following please...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. Thanks!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
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.
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Let one leg be "x".
The other leg is "x+1"
Let the hypotenuse be "h"
EQUATION:
Perimeter: x+x+1+h=12 ft.
1st: 2x+h=11
Pythagoras: x^2+(x+1)^2=h^2
x^2+x^2+2x+1=h^2
2x^2+2x+1 = h^2
2nd: h=sqrt(2x^2+2x+1)
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Solve 1st for h:
3rd: h=-2x+11
Substitute for "h" in 2nd:
-2x+11=sqrt(2x^2+2x+1)
Square both sides to get:
4x^2-44x+121 = 2x^2+2x+1
2x^2-46x+120=0
x^2-23x+60=0
(x-20)(x-3)=0
x-20 or x=3
If x=20 cannot be an answer because the perimeter is 12.
If x=3, h=-2(3)+11 = 5 ft
Hypotenuse is 5 ft.
Cheers,
Stan H.