Question 76179: I need to find three sides of a right triangle by using the pythagorean theorem. The info I have is: leg1: x, leg2: 40-(2x+2), hypotenuse: x+2.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! I need to find three sides of a right triangle by using the pythagorean theorem. The info I have is: leg1: x, leg2: 40-(2x+2), hypotenuse: x+2.
:
If you find x, we can find all three sides:
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a^2 + b^2 = c^2
x^2 + (40 -(2x+2))^2 = (x+2)^2
x^2 + (40 - 2 -2x)^2 = (x+2)^2
x^2 + (38 - 2x)^2 = (x+2)^2
x^2 + 1444 - 152x + 4x^2 = x^2 + 4x + 4
x^2 + 4x^2 - x^2 - 152x - 4x + 1444 - 4 = 0
4x^2 - 156x + 1440 = 0
:
Divide equation by 4
x^2 - 39x + 360 = 0
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Factors to:
(x - 15)(x - 24) = 0
x = +15
x = +24
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Leg 1 = 15;
Leg 2 = 40 -(2(15) + 2 = 40 - 32 = 8
Leg 3 = 15 + 2 = 17
:
Check: 15^2 + 8^2 = 17^2
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Leg 1 = 24
Leg 2 = 40 -(2(24) + 2) = 40 - 50 = -10 so, x = 24 is not a solution
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