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 Answer: the perimeter of the triangle is: P = 30
