SOLUTION: A right triangle has sides with integer lengths. The product of the legs is 120. The sum of the three sides is 40. What are the lengths of the three sides of the triangle?

Question 194729: A right triangle has sides with integer lengths. The product of the legs is 120. The sum of the three sides is 40. What are the lengths of the three sides of the triangle?
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
1) xy =120,,, given two legs product =120
2) x^2 +y^2 = z^2 (pythagorous) (z=hypotenuse)
3) x +y+z= 40,,,,,given
4) sides are integers,,,,given
.
checking all of the factors of 120,, for even integer for z if z^2 = x^2 + y^2
.
only the 8 - 15 - 17 , rt triangle sides fit
.
checking : sum = 40,,ok
.
factors of 120, 1*120, 2*60, 3*40, 4*30, 5* 24, 6* 20, 8*15, 10*12
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