SOLUTION: the hypotenuse of a right triangle is 65 cm. one side is 10 cm shorter than twice the other side. find the lengths of the two sides

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Question 940969: the hypotenuse of a right triangle is 65 cm. one side is 10 cm shorter than twice the other side. find the lengths of the two sides
Answer by nerdybill(7384) About Me  (Show Source):
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the hypotenuse of a right triangle is 65 cm. one side is 10 cm shorter than twice the other side. find the lengths of the two sides
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Let x = side
then from "one side is 10 cm shorter than twice the other side" we have
2x-10 = second side
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apply Pythagorean theorem:
x^2 + (2x-10)^2 = 65^2
x^2 + (2x-10)(2x-10) = 4225
x^2 + 4x^2-20x-20x+100 = 4225
x^2 + 4x^2-40x+100 = 4225
5x^2-40x+100 = 4225
x^2-8x+20 = 845
x^2-8x-825 = 0
factoring the left:
(x+25)(x-33) = 0
x = {-25, 33}
throw out the negative leaving:
x = 33 cm (one side)
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second side:
2x-10 = 2(33)-10 = 66-10 = 56 cm
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answer: 33 cm and 56 cm