SOLUTION: An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has measure (x + 5) cm. Find x. I know that a^2+b^2=c^2 therefore (x+1)(x+1)+(x+1)(x+1)=(x+

Algebra ->  Pythagorean-theorem -> SOLUTION: An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has measure (x + 5) cm. Find x. I know that a^2+b^2=c^2 therefore (x+1)(x+1)+(x+1)(x+1)=(x+      Log On


   

Question 789883: An isosceles right triangle has legs measuring (x + 1) cm each. The hypotenuse has measure (x + 5) cm. Find x.
I know that a^2+b^2=c^2
therefore
(x+1)(x+1)+(x+1)(x+1)=(x+5)(x+5)
x^2+2x+1+x^2+2x+1=x^2+10x+25
2x^2+4x+2=x^2+10x+25

If I put all the variables on one side like this:
x^2-6x=23
I'm not sure what do next or if that is the right thing to do.
Answer by stanbon(75887) About Me  (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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(x+1)^2 + (x+1)^2 = (x+5)^2
x^2 + 2x+1 + x^2 + 2x + 1 = x^2 + 10x + 25
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x^2 -6x -23 = 0
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Use the quadratic formula to get:
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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