SOLUTION: What is the perimeter of a 45°-45°-90° triangle if the hypotenuse is equal to 16 feet?

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Question 821288: What is the perimeter of a 45°-45°-90° triangle if the hypotenuse is equal to 16 feet?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
That is an isosceles right triangle.
The sides opposite the congruent 45%5Eo angles are congruent.
Those are the legs of the right triangle.
If the length of each of those legs is xfeet ,
and the hypotenuse measures 16feet ,
then according to the Pythagorean theorem
x%5E2%2Bx%5E2=16%5E2
2x%5E2=16%5E2
x%5E2=16%5E2%2F2
x%5E2=%288%2A2%29%5E2%2F2
x%5E2=8%5E2%2A2%5E2%2F2
x%5E2=8%5E2%2A2
x=sqrt%288%5E2%2A2%29
x=8sqrt%282%29
The, the perimeter is
8sqrt%282%29%2B8sqrt%282%29%2B16=16sqrt%282%29%2B16=highlight%2816%281%2Bsqrt%282%29%29%29=highlight%28about38.6%29 (rounded)
So the perimeter is about highlight%2838.6feet%29 .