# How to find the side of the square?

Often in geometry it is necessary to find the length of a side of a square, while its parameters are known: perimeter, area, diagonal length.

A square is a rhombus or a rectangle whose sides are equal to each other. The corners of the square are also equal to each other and have 90 ° each. Consider how to find the side of the square with one of the above parameters.

## Finding the side of the square around its perimeter

In this case, to find the length of the side of the square, you need to divide the number of the perimeter of the square by 4 (since the square has 4 sides equal to each other): z = P / 4, where z is the length of the side of the square; P is the perimeter of the square.

The unit of measurement for one side of a square will be the same unit of length as its perimeter. For example, if the perimeter of a square is specified in millimeters, then also the length of its side will be in millimeters.

For example: The perimeter of the square is 40 meters. When solving this problem, we get: z = 40/4 = 10. The length of the side of the square is 10 meters.

## Finding the side of a square by its area

In this case, to find the length of the side, it is necessary to extract the square root of the number of the area value (since the area of the square is equal to the square of its side): z = vS, where z is the length of the side of the square; S is the area of a square.

The unit of measurement for one side of a square will be the same unit of length as its area. For example, if a square is specified in square millimeters, the length of its side will be simply in millimeters.

For example: The area of the square is 16 square meters. In solving this problem, we obtain: z = v9 = 3. The length of the side of the square is 4 meters.

## Finding the side of a square on its diagonal

In this case, the length of the side of the square will be equal to the length of the diagonal of the square divided by the square root of 2 (beyond the Pythagorean theorem, since the adjacent sides of the square and its diagonal are an isosceles right triangle). To find the side of the square diagonally, it is necessary: z = d / v2 (since z2+ z2= d2), where: z is the length of the side of the square; d is the length of the diagonal of the square.

The unit of measurement for one side of a square will be the same unit of length as its diagonal. For example, if the diagonal of a square is given in millimeters, then also the length of its side will be in millimeters.

For example: The diagonal of a square is 20 meters.When solving this problem, we obtain: z = 20 / v2, this is approximately equal to 20 / 1.4142. The length of the side of the square is 20 / v2 meters, or approximately 14,142 meters.

Now you know how to find the length of a side of a square, if its perimeter, area or diagonal length is specified.