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SOLUTION: 1. Find the length of a shorter leg of a right triangle if the longer leg is 10 miles more than the shorter leg and the hypotemuse is 10 miles less than twice the shorter leg.
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-> SOLUTION: 1. Find the length of a shorter leg of a right triangle if the longer leg is 10 miles more than the shorter leg and the hypotemuse is 10 miles less than twice the shorter leg.
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Question 78065
:
1. Find the length of a shorter leg of a right triangle if the longer leg is 10 miles more than the shorter leg and the hypotemuse is 10 miles less than twice the shorter leg.
Answer by
stanbon(69061)
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put this solution on YOUR website!
Find the length of a shorter leg of a right triangle if the longer leg is 10 miles more than the shorter leg and the hypotemuse is 10 miles less than twice the shorter leg.
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Let the length of the shorter leg be "x" miles.
Longer leg is "x+10".
Hypotenuse is "2x-10".
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EQUATION: Use Pythagoras to get:
x^2 + (x+10)^2= (2x-10)^2
x^2 + x^2+20x+100 = 4(x^2-10x+25)
2x^2+20x+100 = 4x^2-40x+100
2x^2-60x=0
2x(x-30)=0
x=30 (this is the length of the shorter leg)
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cheers,
Stan H.