# The area of a rectangle is 100 square inches. The perimeter of the rectangle is 40 inches.? A second rectangle has the same area but a different perimeter. Is the second rectangle a square?

##### 1 Answer

No. The second rectangle is not a square.

#### Explanation:

The reason why the second rectangle isn't a square is because the first rectangle is the square. For instance, if the first rectangle (a.k.a. the square) has a perimeter of

With this being said, let's justify the statement above. If the first rectangle is indeed a square* then all of it's sides must be equal.

Moreover, this would actually make sense for the reason that if one of its sides is

Also, this would mean that the area must be

To clarify, what this means is that there wouldn't possible be a way of getting a square with an area of

In conclusion, that is why the second rectangle isn't (and can't be) a square.

*A square can be a rectangle, but a rectangle can't be a square so, the first rectangle was originally a square.