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

Let x represent the length of the original square in inches. Thus the area of the original square is x2. Two inches are added to x, which is represented by x+2. The area of the resulting square is (x+2)2. We are given that the new square is 64 sq. inches greater than the original. Therefore we can write the algebraic expression:

x2 + 64 = (x+2)2

FOIL the right side of the equation.

x2 + 64 = x2 + 4x + 4

Subtract x2 from both sides and then continue with the alegbra.

64 = 4x + 4

64 = 4(x + 1)

16 = x + 1

15 = x

Therefore, the length of the original square is 15 inches.

If you plug in the answer choices, you would need to add 2 inches to the value of the answer choice and then take the difference of two squares. The choice with 15 would be correct because 172 -152 = 64.

The area of a square is equal to length times width or length squared (since length and width are equal on a square). Therefore, the length of one side is l = $$\sqrt{25in^{2}$$} or l=5 in. The perimeter of a square is the sum of the length of all 4 sides or 4 times 5 in. =20 in.

Given that the square's diagonals pass through the circle's center, those diagonals must each form a diameter of the circle. The circle's diameter is twice its radius, i.e. , which is . Since this diameter (i.e., the square's diagonal) is the hypotenuse of a right triangle formed by two sides of the square, the length of one of the square's sides can be calculated with the Pythagorean Theorem. replace and because the sides of the square must be equal in length. Since the objective is to solve for the square's area, solve for since one side squared will be the square's area.

units squared

We start by dividing the area of square R (48) by 12, to come up with the area of square T, 4. Then take the square root of the area to get the length of one side, giving us 2.

Let x represent the length of the original square in inches. Thus the area of the original square is x2. Two inches are added to x, which is represented by x+2. The area of the resulting square is (x+2)2. We are given that the new square is 64 sq. inches greater than the original. Therefore we can write the algebraic expression:

x2 + 64 = (x+2)2

FOIL the right side of the equation.

x2 + 64 = x2 + 4x + 4

Subtract x2 from both sides and then continue with the alegbra.

64 = 4x + 4

64 = 4(x + 1)

16 = x + 1

15 = x

Therefore, the length of the original square is 15 inches.

If you plug in the answer choices, you would need to add 2 inches to the value of the answer choice and then take the difference of two squares. The choice with 15 would be correct because 172 -152 = 64.

The area of a square is equal to length times width or length squared (since length and width are equal on a square). Therefore, the length of one side is l = $$\sqrt{25in^{2}$$} or l=5 in. The perimeter of a square is the sum of the length of all 4 sides or 4 times 5 in. =20 in.

Given that the square's diagonals pass through the circle's center, those diagonals must each form a diameter of the circle. The circle's diameter is twice its radius, i.e. , which is . Since this diameter (i.e., the square's diagonal) is the hypotenuse of a right triangle formed by two sides of the square, the length of one of the square's sides can be calculated with the Pythagorean Theorem. replace and because the sides of the square must be equal in length. Since the objective is to solve for the square's area, solve for since one side squared will be the square's area.

units squared

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, .

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.

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