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Question 1008204: The hypotenuse of a right triangle is 1 centimeter more than twice the length of the shorter leg, and the longer leg is 9 centimeters shorter than 3 times the length of the shorter leg. Find the length of the three sides of the triangle.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! smallest leg = x
hypotenuse = 2x+1
largest leg = 3x-9
by pythagorus:
(x^2 + (3x-9)^2 = (2x+1)^2
simplify to get:
x^2 + 9x^2 - 54x + 81 = x^2 + 4x + 1
subtract all the terms on the right side of the equation from both sides of the equation to get:
x^2 + 9x^2 - 54x + 81 - x^2 - 4x - 1 = 0
combine like terms to get:
6x^2 - 58x + 80 = 0
factor the quadratic to get:
x = 1 and 1/3 or x = 8
when x = 8:
the smallest leg = 8
the largest leg = 15
the hypotenuse = 17
when x = 1 and 1/3:
the smallest leg = 1 and 1/3
the largest leg = -4
the hypotenuse = 4 and 1/3.
since all legs of the triangle have to be greated than 0, then x can't be 1 and 1/3.
that leaves x = 8.
the length of the three sides of the triangle are 8, 15, 17.
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