A triangle has one leg that is 3 inches longer than the other leg. The hypotenues is 15 inches

Answer 1

15^2 = 225

225 = S^2 + (S+3)^2 = 2S^2 + 6S + 9

rearrange terms and solve the quadratic for S, the smaller leg

S^2 + S^2 + 6S + 9 = 225

2S^2 + 6S - 116 = 0

factor or use the quadratic formula

Or much faster & easier is to recognize this is a 3-4-5 right triangle, inflated by a factor of 3, so

it's a 9-12- 15 triangle, with 2 sides 9 and 12, one 3 more than the other

15^2 = 12^2 + 9^2

225 = 144 + 81 = 225