The longer leg of a right triangle is 7 cm longer than the shorter leg. the hypotenuse is 8 cm longer than the shorter leg. what is the perimeter of the triangle?

First we define a variable:
 x: length of the shortest side of the triangle.
 Then, using the Pythagorean theorem we have:
 (x + 8) ^ 2 = x ^ 2 + (x + 7) ^ 2
 Rewriting we have:
 x ^ 2 + 16x + 64 = x ^ 2 + x ^ 2 + 14x + 49
 Clearing x we have:
 64 - 49 = 2x ^ 2 - x ^ 2 + 14x - 16x
 64 - 49 = 2x ^ 2 - x ^ 2 + 14x - 16x
 15 = x ^ 2 - 2x
 x ^ 2 - 2x - 15 = 0
 The roots of the polynomial are:
 x = -3
 x = 5
 We discard the negative root because it is a dimension.
 Then, the perimeter is:
 P = (x + 7) + (x + 8) + x
 P = (5 + 7) + (5 + 8) + 5
 P = 30
 
 the perimeter of the triangle is:
 P = 30

2x+3(6)=36
2x+18=36
subtract 18 both sides
2x=18
x=9