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No. Take a square with each side 9 feet long. The perimeter is 9+9+9+9 = 36 ft and the area is 9 x 9 = 81 square feet.

Now squash the square down a bit so that it is a 7 x 11 rectangle. The perimeter is still 36 ft, but the area is now smaller at 77 square feet.

Squash it right down to just 1 ft tall by 17 ft wide and the perimeter is still 36 ft, but the area is now just 17 square feet.

So for any given perimeter, the closer the shape of a rectangle is to a square, the larger will be the area.

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Q: Do the two rectangles with the same perimeter always have the same area?
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