If a=side of the square in feet, then the width of the rectangular dance floor is a-10 and its length is a+15. The perimeter is twice the length plus twice the width=2(a-10+a+15)=130, so 2a+5=65, and a=(65-5)/2=30. The length and width of the dance floor are respectively 30+15=45 feet and 30-10=20 feet.
Also since the area of the rectangular floor equals the area of the square floor: (a-10)(a+15)=a^2⇒a^2+5a-150=a^2, so the a^2 cancel out and 5a=150, from which a=30. It wasn't necessary to supply the perimeter as well.