**Perimeter of Square :**

In this section, we are going to learn, how to find perimeter of a square.

A square is a four-sided closed figure where the lengths of all the four sides will be equal and each vertex angle will be right angle or 90^{o }as shown below.

Let s be the length of each side of a square.

Then, the formula for perimeter of a square :

**Perimeter = 4s**

**Example 1:**

Find the perimeter of the square having side length 14 cm.

**Solution:**

Formula for perimeter of a square :

= 4s^{ }

Substitute 14 for s.

= 4(14)

= 56

So, the perimeter of the square is 56 cm.

**Example 2:**

If the perimeter of square is 32 inches, then find the length of each side.

**Solution:**

Perimeter of the square = 32 inches

4s = 32

Divide each side by 4.

s = 8

So, the length of each side of the square is 8 inches.

**Example 3 :**

The square has side length 250 cm. Find its perimeter in meter.

**Solution:**

Formula for perimeter of a square :

= 4s^{ }

Substitute 250 for s.

= 4(250)

= 1000 cm -----(1)

We know

100 cm = 1 m

Therefore, to convert centimeter into meter, we have to divide by 100.

(1)-----> Perimeter = 1000 cm

Divide the right side by 100 to convert cm into m.

Perimeter = (1000 / 100) m

= 10 m

So, the perimeter of the square is 10 meters.

**Example 4:**

If the length of each diagonal of a square is 2√2 cm, then find its perimeter.

**Solution:**

To find the perimeter of a square, first we have to know the length of each side.

Let s be the length of each side of the square.

Draw a sketch.

In the figure shown above, consider the right triangle ABC.

By Pythagorean Theorem, we have

AB^{2} + BC^{2} = AC^{2}

Substitute.

s^{2} + s^{2} = (2√2)^{2}

Simplify and solve for s.

2s^{2} = 2^{2} ⋅(√2)^{2}

2s^{2} = 4 ⋅(2)

2s^{2} = 8

Divide each side by 2.

s^{2} = 4

Find positive square root on both sides.

√s^{2} = √4

√s^{2} = √(2 ⋅ 2)

s = 2

Formula for perimeter of a square.

Perimeter = 4s

Substitute 2 for s.

= 4(2)

= 8

So, the perimeter of the square is 8 cm.

**Example 5:**

If the lengths of the sides of two squares are in the ratio 2 : 5. then find the ratio of their perimeters.

**Solution:**

From the ratio 2 : 5, let the sides of two squares be 2x and 5x respectively.

Formula for perimeter of a square :

= 4s

= 4(2x) = 8x |
= 4(5x) = 10x |

Ratio of the perimeters :

= 8x : 10x

Divide each term by 2x.

= 2 : 5

So, the ratio of the perimeters of two squares is 2 : 5.

**Note :**

The ratio of the sides of two squares and the ratio of the perimeters of two squares are same.

After having gone through the stuff given above, we hope that the students would have understood, "Perimeter of Square".

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