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In a right triangle, the hypotenuse is 65 and the altitude to the hypotenuse is 300/13.  Find the legs of the right triangle.

 Jun 28, 2020
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In a right triangle, the hypotenuse is 65 and the altitude to the hypotenuse is 300/13. Find the legs of the right triangle.

 

We first want to find the area of the triangle, which is \((65*300/13)/2 = 750\)

Note that we divide by two since this is a triangle. We could set up an algebraic equation to solve for the legs, but by some observation, we can find that this is a 25-60-65 triangle, with the area being 750 and the squares of the bases summing to to the hypotenuse's square.

Thus the legs of the right triangle are 25 and 60

I hope this helped.

 Jun 28, 2020

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