SOLUTION: The perimeter of a right triangle is 60 cm. The length of the hypotenuse is 6 cm more than twice the length of one of the other sides. Find the length of all three sides.

Question 961234: The perimeter of a right triangle is 60 cm. The length of the hypotenuse is 6 cm more than twice the length of one of the other sides. Find the length of all three sides.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
The perimeter of a right triangle is 60 cm. The length of the hypotenuse is 6 cm more than twice the length of one of the other sides. Find the length of all three sides.
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let x=one of the sides
2x+6=hypotenuse
other side=√((2x+6)^2-x^2)=√(4x^2+24x+36-x^2)=√(3x^2+24x+36)
..
x+(2x+6)+√(3x^2+24x+36)=60
√(3x^2+24x+36)=54-3x
square both sides
3x^2+24x+36=2916-324x+9x2
6x^2-348x+2880=0
x^2-58x+480=0
(x-10)(x-48)=0
x=48(reject, extraneous root)
x=10
2x+6=26
√(3x^2+24x+36)=√(300+240+36)=√576=24
..
one of the sides=10
hypotenuse=26
other side=24

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