Question 194729
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
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checking  all  of  the  factors  of  120,,  for  even  integer  for  z if  z^2 = x^2 + y^2
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only  the  8 - 15 - 17 ,  rt  triangle  sides  fit
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checking :  sum  =  40,,ok
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factors  of  120, 1*120, 2*60, 3*40, 4*30, 5* 24, 6* 20, 8*15, 10*12