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.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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.       Log On


   

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) About Me  (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.