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Question

A dance floor is made from square wooden tiles with a side length of 1 foot. The floor can be laid out as a square or rectangle. The width of the Dane floor is 10 feet less than the width of a square dance floor,and its length is 15 feet greater than the length of the square floor. The perimeter of the rectangle floor is 130 feet

Answer 1

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.