How to find the length of the side of a square - Math

The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:

(a) A square with area square inches has sidelength inches.

(b) A square with perimeter inches has sidelength inches.

(a) is the greater quantity.

The sidelength of a square is the square root of its area and one-fourth of its perimeter, so:

(a) A square with area 400 square inches has sidelength inches.

(b) A square with perimeter 80 inches has sidelength inches.

The two quantities are equal.

Divide the perimeter of a square by 4 to get its sidelength:

One of the necessary conditions of a square is that all sides be of equal length. Therefore, because we are given the length of one side we know the length of all sides and that includes the length of the opposite side. Since the length of one of the sides is 4 we can conclude that all of the sides are 4, meaning the opposite side has a length of 4.

To solve, simply use the formula for the area of a square to solve for side length. Thus,

The sides can be found by taking the square root of the area.

, where = side.

.

So the length of a side is 6.3 cm.

First, know that all the side lengths of a square are equal. Second, know that the sum of all 4 side lengths gives us the perimeter. Thus, the square perimeter of 16 is written as

where S is the side length of a square. Solve for this S

So the length of each side of this square is 4.

The area of any quadrilateral can be determined by multiplying the length of its base by its height.

Since we know the shape here is square, we know that all sides are of equal length. From this we can work backwards by taking the square root of the area to find the length of one side.

The length of one (and each) side of this square is 6 inches.

We will have two formulas to help us solve this problem, the area and perimeter of a square.

The area of a square is:

,

where length of the square and width of the square.

The perimeter of a square is:

Plugging in our values, we have:

Since all sides of a square have the same value, we can replace all and with (side). Our equations become:

Therefore, .

We begin by recalling the formulas for the perimeter and area of a square respectively.

Using these formulas and the fact that the perimeter is half the area, we can create an equation.

We can multiply both sides by 2 to eliminate the fraction.

To get one side of the equation equal to zero, we will move everything to the right side.

Next we can factor.

Setting each factor equal to zero provides two potential solutions.

or

However, since a square cannot have a side of length 0, 8 is our only answer.

If diagonal of Square is constructed, then is a 45-45-90 triangle with hypotenuse . By the 45-45-90 Theorem, the sidelength can be calculated as follows:

.

The diameter of a circle with circumference 20 is

The diameter of a circle that circumscribes a square is equal to the length of the diagonals of the square.

If diagonal of Square is constructed, then is a 45-45-90 triangle with hypotenuse approximately 6.3662. By the 45-45-90 Theorem, divide this by to get the sidelength of the square:

The diameter of a circle that is inscribed inside a square is equal to its sidelength , so all we need to do is find the diameter of the circle - which is circumference 16 divided by :

.

Let , the sidelength shared by the square and the equilateral triangle.

The area of is

The area of Square is .

By symmetry, bisects the portion of the square not in the triangle, so the area of Quadrilateral is half the difference of those of the square and the triangle. Since the area of Quadrilateral is 100, we can set up an equation:

Of the five choices, 20 comes closest.

The area of Square is the square of sidelength , or .

The area of Rectangle is . Rectangle has area 90% of that of Square , which is ; is 80% of , so . We can set up the following equation:

As a percent, of is

The area of the square was originally

,

being the sidelength.

Reducing the area by 12% means that the new area is 88% of the original area, or ; the square root of this is the new sidelength, so

Each side of the new square will measure 94% of the length of the old measure - a reduction by 6%.

Recall how to find the perimeter of a square:

By dividing both sides by , we can write the following:

For the square in question,

Recall how to find the perimeter of a square:

By dividing both sides by , we can write the following:

For the square in question,

Recall how to find the perimeter of a square:

By dividing both sides by , we can write the following:

For the square in question,