How to find the length of the side of a square

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

Questions 1 - 10

Which is the greater quantity?

(a) The sidelength of a square with area square inches.

(b) The sidelength of a square with perimeter inches.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

It is impossible to tell which is greater from the information given.

Explanation

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 $\sqrt{225} = 15$ inches.

(b) A square with perimeter inches has sidelength $50 \div 4 = 12.5$ inches.

(a) is the greater quantity.

If the area of a square is , find the length of one side of the square.

Explanation

Recall how to find the area of a square:

$\text{Area}=\text{side length}^2$

We can rewrite that equation into the following:

$\text{side length}=\sqrt{\text{Area}}$

Now, plug in the given area to find the side length of the square.

$\text{Side length}=\sqrt{784}=28$

True or false: A square with area 49 has sides of length 7.

True

False

Explanation

Given the length of each side of a square, the area of the square is the square of this length. Therefore, to find the sidelength, take the square root of the area. The area of the square is 49, and $7^{2} = 7 \times 7 = 49$ , so its sidelength is $\sqrt{49} = 7$ .

Find the side length of a square given the area is 144.

Explanation

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

$A=s^2\Rightarrow s=\sqrt{A}$

$s=\sqrt{144}=12$

Oscar recently built his first home, with a floor plan that is both a perfect square and has an area of . What is the length for the sides of Oscar's new home?

Explanation

Since both sides of a square are of equal length, we can use this formula to determine the length of both sides.

$\Area=length\cdot length\ 729;ft^2=length^2\length=\sqrt{729;ft^2}\length=27;ft$

If the diagonal of a square is , what is the length of one side of the square?

$5\sqrt2$

$10\sqrt2$

Explanation

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{10}{\sqrt{2}}=\frac{10\sqrt2}{2}=5\sqrt2$

Multiply the top and bottom of the fraction by one in the form of $\frac{\sqrt{2}}{\sqrt{2}}$

$\text{Side length}=\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

Silve.

$\text{Side length}=\frac{10\sqrt2}{2}$

Simplify.

$\text{Side length}=5\sqrt2$

If the diagonal of the square is $4\sqrt2$ , what is the length of one side of the square?

$4\sqrt2$

$2\sqrt2$

Explanation

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{4\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=4$

A playground is enclosed by a square fence. The area of the playground is . The perimeter of the fence is . What is the length of one side of the fence?