SOLUTION: Quadratic equation
6. The length of one leg of a right triangle is 7 cm more than that of the other leg. The length of the hypotenuse is 3 cm more than double that of the shorter
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Question 198333: Quadratic equation
6. The length of one leg of a right triangle is 7 cm more than that of the other leg. The length of the hypotenuse is 3 cm more than double that of the shorter leg. Find the lengths of each of the three sides.
Thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The length of one leg of a right triangle is 7 cm more than that of the other leg. The length of the hypotenuse is 3 cm more than double that of the shorter leg. Find the lengths of each of the three sides.
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shorter leg : x
longer leg : x+7
hypotenuse: 2x +3
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Equation:
leg^2 + leg^2 = hypotenuse^2
x^2 + (x+7)^2 = (2x+3)^2
x^2 + x^2 + 14x + 49 = 4x^2 + 12x + 9
2x^2 -2x - 40 = 0
x^2 - x - 20 = 0
(x-5)(x+4) = 0
Positive solution:
x = 5 (shorter leg)
x+7 = 12 (longer leg)
2x+3 = 13 (hypotenuse)
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Cheers,
Stan H.
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