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,

**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 to 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.

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