SOLUTION: An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has measure (x + 5) cm. Find x.
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Question 658610: An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has measure (x + 5) cm. Find x. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has measure (x + 5) cm. Find x.
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Use Pythagoras:
2(x+1)^2 = (x+5)^2
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2[x^2 + 2x + 1] = x^2 + 10x + 25
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2x^2 + 4x + 2 = x^2 + 10x + 25
x^2 -6x -23 = 0
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x = [6 +- sqrt(36 - 4*-23)]/2
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x = [6 +- sqrt(128)]/2
x = [6 +- 8sqrt(2)]/2
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Positive solution:
x = 3 + 4sqrt(2)
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Cheers,
Stan H.
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