SOLUTION: an isoceles triangle has a hypotenuse 15 cm long. Determine the length of the two equal sides? thnxx

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Question 180768: an isoceles triangle has a hypotenuse 15 cm long. Determine the length of the two equal sides?
thnxx
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Since there's a hypotenuse, this means that the triangle must be a right triangle.


So we basically have this triangle set up:


drawing%28500%2C500%2C-0.5%2C2%2C-0.5%2C3.2%2C%0D%0Aline%280%2C0%2C0%2C3%29%2C%0D%0Aline%280%2C3%2C2%2C0%29%2C%0D%0Aline%282%2C0%2C0%2C0%29%2C%0D%0Alocate%28-0.2%2C1.5%2Cx%29%2C%0D%0Alocate%281%2C-0.2%2Cx%29%2C%0D%0Alocate%281%2C2%2C15%29%0D%0A%29


Since the legs are x and x this means that a=x and b=x


Also, since the hypotenuse is 15, this means that c=15.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


x%5E2%2Bx%5E2=15%5E2 Plug in a=x, b=x, c=15


x%5E2%2Bx%5E2=225 Square 15 to get 225.


2x%5E2=225 Combine like terms.


x%5E2=225%2F2 Divide both sides by 2.


x=sqrt%28225%2F2%29 Take the square root of both sides. Note: we're only dealing with the positive square root.


x=%2815%2Asqrt%282%29%29%2F2 Simplify the square root.


x=10.61 Approximate


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Answer:


So the solution is approximately x=10.61 which means that the length of the two equal sides is about 10.61 cm

Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
an isoceles triangle has a hypotenuse 15 cm long. Determine the length of the two equal sides?
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Let each of the equal sides have length "x"
15^2 = x^2 + x^2
2x^2 = 15^2
x = (15/2)sqrt(2)


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Cheers,
Stan H.