Question

A rectangle has the same perimeter as a square. If the area of the rectangle is 9 less than the area of the square, the side length of the square is how much longer than the shorter side of the rectangle ?

Answer 1

xy = s^2-9 = (s-3)(s+3)

Looks like the rectangle has short side x=s-3, so s = x+3

p(rect) = 2(s-3)+ 2(s+3) = 4s = p(square)

there are lots of solutions
3x9 : 6x6
17x23 : 20x20
...