SOLUTION: In a right triangle, the hypotenuse is 1 foot more than twice the shortest side. The other side is 1 foot less than twice the shortest side. What is the length of the shortest si

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Question 88241: In a right triangle, the hypotenuse is 1 foot more than twice the shortest side. The other side is 1 foot less than twice the shortest side. What is the length of the shortest side?
Answer by stanbon(75887) About Me  (Show Source):
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In a right triangle, the hypotenuse is 1 foot more than twice the shortest side. The other side is 1 foot less than twice the shortest side. What is the length of the shortest side?
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Let the shortest side be x.
Hypotenuse = 2x+1
3rd side = 2x-1
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Using Pythagoras you get:
(2x+1)^2 = x^2 + (2x-1)^2
4x^2+4x+1 = x^2 + 4x^2-4x+1
x^2-8x=0
x(x-8)=0
x=0 or x=8
Reasonable answer: x=8 (shortest side)
2x+1 = 17 (hypotenuse)
2x-1 = 15 (3rd side)
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Cheeers,
Stan H.