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Is this a trick question? A square with a perimeter of 5 feet and an area of 5 square feet cannot exist. Let's see why. If a square has a perimeter of 5 feet, that means the sum of the lengths of the four sides is 5 feet. The four sides are of equal length (it's a square), and the sum of the four (equal) lengths is 5 feet, then each side is (5 feet divided by 4) in length. That's 1 1/4 feet for each side. The area will be the square of the length of a side or 1 1/4 squared, which will be 25/16 or 1 9/16 square feet in area. If a square has an area of 5 square feet, the length of a side will be the square root of the area. The square root of five is about 2.236, so each side will be about 2.236 feet in length. It's perimeter will about 8.944 feet. With the math working the way it did there, it makes it kinda hard to have a square with a perimeter of 5 feet and an area of 5 square feet. But don't bounce yet. As an aside (but a related one) let's estimate the answers. First, if a square has a perimeter of 5 feet, it's four (equal) sides will sum to the 5 feet. The 5 divided by 4 is a little over one, so each side is a little over 1 foot long. The area of a square with a side a little over 1 foot long will be the square of the length of one side or (1+ a little bit times 1+ a little bit) which will be equal to 1+ a little more than a little square feet for the area. Make sense? Onward. If a square has an area of 5 square feet, a side will be the square root of 5 feet long. If we consider the square of 2 is 4, the it will take the square of 2+ a little bit to equal 5 square feet. Got that? Now we bounce.

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Q: If a square has a perimeter of 5 feet and an area of 5 square feet how long is a side?
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