SOLUTION: The perimeter of a right triangle is 60 cm .Its hypotenuse s 26cm. find the other two sides and the area of the triangle.

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Question 975492: The perimeter of a right triangle is 60 cm .Its hypotenuse s 26cm. find the other two sides and the area of the triangle.
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
x, y, h for the two legs and the Hypotenuse.

system%28x%2By%2Bh=60%2Cx%5E2%2By%5E2=h%5E2%29 and h is given.

system%28x%2By%2B26=60%2Cx%5E2%2By%5E2=%2826%29%5E2%29

system%28x%2By=36%2Cx%5E2%2By%5E2=676%29

x%5E2%2B%2836-x%29%5E2=676

x%5E2%2B36%5E2-72x%2Bx%5E2-676=0

2x%5E2-72x%2B1296-676=0

2x%5E2-72x%2B620=0

x%5E2-36x%2B310=0

x=%2836%2B-+sqrt%2856%29%29%2F2

x=%2836%2B-+2%2Asqrt%2814%29%29%2F2

highlight%28x=18%2B-+sqrt%2814%29%29

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Dimensions are highlight%2818-sqrt%2814%29%29 and 36-%2818-sqrt%2814%29%29=highlight%2818%2Bsqrt%2814%29%29.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If the perimeter is 60 and the hypotenuse is 26, then the sum of the other two sides must be 34. Let represent the measure of one of the two legs and then will represent the measure of the other leg, allowing us to state the pythagorean relationship:



Expand, collect like terms, put the quadratic in standard form, and solve (hint: it factors). The two roots of the equation represent the measures of the two legs of the triangle. The area of a right triangle is the product of the legs divided by 2.

John

My calculator said it, I believe it, that settles it