**Perimeter of Square Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on perimeter of square.

Before look at the worksheet, if you wish to learn the stuff perimeter of square,

**Problem 1 :**

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

**Problem 2 :**

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

**Problem 3 :**

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

**Problem 4 :**

The length of each side of a square is 48 inches. Find its perimeter in feet.

**Problem 5 :**

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

**Problem 6 :**

If the area of a square is 49 square inches, then find its perimeter.

**Problem 7 :**

Find the perimeter of the figure which has the following vertices in xy-coordinate plane.

E(-1, 3), F(4, 3), G(4, -2) and H(-1, -2)

**Problem 8 :**

PQ is one of the sides of the square PQRS and the side PQ is defined by P(0, 2) and Q(6, 9). Find the perimeter of the square PQRS.

**Problem 9 :**

AC is one of the diagonals of the square ABCD and the diagonal AC is defined by A(1, 4) and C(4, 8). Find the perimeter of the square ABCD.

**Problem 10 :**

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

**Problem 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.

**Problem 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.

**Problem 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.

**Problem 4 :**

The length of each side of a square is 48 inches. Find its perimeter in feet.

**Solution : **

Formula for perimeter of a square :

= 4s^{ }

Substitute 48 for s.

= 4(48)

= 192 inches -----(1)

We know

12 inches = 1 ft

Therefore, to convert inches into feet, we have to divide by 12.

(1)-----> Perimeter = 192 inches

Divide the right side by 12 to convert inches into ft.

Perimeter = (192 / 12) ft

= 16 ft

So, the perimeter of the square is 16 ft.

**Problem 5 :**

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 the square is 8 cm.

**Problem 6 :**

If the area of a square is 49 square inches, then find its perimeter.

**Solution:**

Area of the square = 49 square inches

s^{2} = 49

Find positive square root on both sides.

√s^{2} = √49

√s^{2} = √(7 ⋅ 7)

s = 7

Formula for perimeter of a square :

= 4s

Substitute 7 for s.

= 4(7)

= 28

So, the perimeter of the square is 28 inches.

**Problem 7 :**

Find the perimeter of the figure which has the following vertices in xy-coordinate plane.

E(-1, 3), F(4, 3), G(4, -2) and H(-1, -2)

**Solution:**

Draw a sketch with the given vertices.

Clearly, the above figure is a square with side length of 5 units.

Formula for perimeter of a square :

= 4s

Substitute 5 for s.

= 4(5)

= 20

So, the perimeter of the square is 20 units.

**Problem 8 :**

PQ is one of the sides of the square PQRS and the side PQ is defined by P(0, 2) and Q(6, 9). Find the perimeter of the square PQRS.

**Solution:**

**Distance between the two points (x _{1}, y_{1}) and (x_{2}, y_{2}) is **

**= √[(x _{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}]**

**To find the distance between P and Q, substitute **

**(x _{1}, y_{1}) = (0, 2)**

**(x _{2}, y_{2}) = (6, 9)**

**in the above formula.**

**Distance between P and Q : **

**= √[(6-0) ^{2 }+ (9-2)^{2}]**

**= √[6 ^{2 }+ 7^{2}]**

**= ****√[36 ^{ }+ 49]**

**= ****√85**

**Therefore, the length of one of the sides is ****√85**** units.**

Formula for perimeter of a square :

= 4s

Substitute s = **√8**5.

= 4**√8**5

Use calculator and simplify.

≈ 36.88

So, the perimeter of the square PQRS is about 36.88 units.

**Problem 9 :**

AC is one of the diagonals of the square ABCD and the diagonal AC is defined by A(1, 4) and C(4, 8). Find the perimeter of the square ABCD.

**Solution : **

**Distance between the two points (x _{1}, y_{1}) and (x_{2}, y_{2}) is **

**= √[(x _{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}]**

**To find the distance between A and C, substitute **

**(x _{1}, y_{1}) = (1, 4)**

**(x _{2}, y_{2}) = (4, 8)**

**in the above formula.**

**Distance between A and C : **

**= √[(4-1) ^{2 }+ (8-4)^{2}]**

**= √[3 ^{2 }+ 4^{2}]**

**= ****√[9 ^{ }+ 16]**

**= ****√25**

**= 5**

**Therefore, the length of the diagonal AC is 5**** units.**

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} = 5^{2}

Simplify and solve for s.

2s^{2} = 25

Divide each side by 2.

s^{2} = 12.5

Find positive square root on both sides.

√s^{2} = √12.5

s = √12.5

Formula for perimeter of a square.

Perimeter = 4s

Substitute √12.5 for s.

= 4√12.5

Use calculator and simplify.

≈ 14.14

So, the perimeter of the the square is about 14.14 units.

**Problem 10 :**

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 Worksheet".

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