PERIMETER OF 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. 

Formula for Perimeter of Square

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

Then, 

Perimeter  =  4s

Examples

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

AB² + BC²  =  AC²

Substitute.

s² + s²  =  (2√2)²

Simplify and solve for s. 

2s²  =  2² ⋅(√2)²

2s²  =  4 ⋅(2)

2s²  =  8

Divide each side by 2. 

s²  =  4

Find positive square root on both sides.

 √s²  =  √4

 √s²  =  √(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

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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