Question

* Lin had a rectangular carpet. It was too large for her living room, and so on each side of the carpet, she cut a stripe 1 foot wide. As a result, the area of the carpet became 26 ft2 smaller. What was the original perimeter of the carpet?

Answer 1

Let the original length of the carpet be L and the original width of the carpet W, then

$LW - 26 = (L - 2)(W - 2)=LW-2L-2W+4 \\ \\ 2L+2W=4+26=30ft$

Therefore, the initial perimeter of the carpet is 30 feet.

Answer 2

30 ft Let's assume the original dimension of the carpet was LxW. Now let's have Lin cut a 1 foot wide strip from the length. That gives her a strip that's L feet long. She then cuts a strip from the other side, giving her another strip that L feet long. She then cuts a strip from the width, giving her a 3rd strip that's (W-2) feet long. And finally, she cuts a 4th strip that's also W-2 feet long. So the total length of all those strips is L + L + W - 2 + W - 2 = 2L + 2W - 4 feet long. And since all the strips are 1 foot wide, they cover 2L + 2W - 4 square feet. So: 2L + 2W - 4 = 26 2L + 2W = 30 Now the original perimeter of the carpet is 2L + 2W, therefore the original perimeter is 30 feet.