SOLUTION: The perimeter of an isosceles triangle is 80cm. What is the length of the hypotenuse. Express your answer in the simplest radical form.

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Question 683743: The perimeter of an isosceles triangle is 80cm. What is the length of the hypotenuse. Express your answer in the simplest radical form.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of an isosceles triangle is 80cm. What is the length of the hypotenuse. Express your answer in the simplest radical form.
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The reference to hypotenuse implies it's a right triangle.
The sides are s, s & h
s%5E2+%2B+s%5E2+=+h%5E2
2s%5E2+=+h%5E2
h+=+s%2Asqrt%282%29
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2s + h = 80
Sub for h
2s+%2B+s%2Asqrt%282%29+=+80
s+=+80%2F%282%2Bsqrt%282%29%29
h+=+s%2Asqrt%282%29+=+80%2Asqrt%282%29%2F%282%2Bsqrt%282%29%29
h+=+80%2Asqrt%282%29%2A%282+-+sqrt%282%29%29%2F2
h+=+40%2Asqrt%282%29%2A%282+-+sqrt%282%29%29
h+=+80%2Asqrt%282%29+-+80%29
h+=+80%2A%28sqrt%282%29+-+1%29%29
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A different way:
Perimeter = P1 of a 1, 1, sqrt(2) triangle = 2 + sqrt(2)
P80 = perimeter of triangle 80
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P1/P80 = (2+sqrt(2))/80 = sqrt(2)/h
h*(2+sqrt(2)) = 80sqrt(2)
Same as above