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.

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(75887) (Show Source): You can 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.
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