How long is the shorter side of a rectangle when one side is 2” longer than the other and the area is 15 sq. in?

Let  x be the shorter side....and x + 2  be the longer side.....so we have

x ( x + 2) = 15

x^2 + 2x = 15     subtract 15 from both sides

x^2 + 2x - 15  = 0   factor

(x - 3) ( x + 5)  = 0

Set each factor to 0 and x  = 3   or  x  = -5  [reject]

So the shorter side = 3 in