AREA AND PERIMETER OF RECTANGLE

Problem 1 :

The area of a rectangle is 42 cm². If its length is 7cm, What is its width ?

Solution :

Given, Area =  42 cm², Length = 7 cm, and width = ?

Area of a rectangle = Length × width

42 = 7 × width

(42)/7 = width

width = 6 cm

Problem 2 :

The perimeter of a square is 32 meters. Find the length of one side of the square.

Solution :

Given, Perimeter = 32 meters.

Perimeter of a square = 4a

(Here a is the length of one side of the square.)

32 = 4a

32/4 = a

a = 8

Problem 3 :

The Length of a rectangle is 13 cm. what is the width if the area is 65 cm² ?

Solution :

Given, Area =  65 cm², Length = 13 cm, and width = ?

Area of a rectangle = Length × width

65 = 13 × width

(65)/13 = width

width = 5 cm

Problem 4 :

The area of a square is 81 mm². What is the length of each side?

Solution :

Given, Area =  81 mm².

Area of a square = a²

(Here a is the length of each side of the square).

81 = a²

a = √81

a = 9 mm

Problem 5 :

The area of a rectangle is 40 cm². If its length is 10 cm, what is its width?

Solution :

Given, Area =  40 cm², length = 10 cm, and width = ?

Area of a rectangle = Length × width

40 = 10 × width

(40)/10 = width

width = 4 cm

Problem 6 :

The perimeter of a rectangle is 200 cm. The rectangle is 3 times longer than wide. What are the length and width of this rectangle ?

Solution :

Given, Perimeter =  200 cm.

Let the width be x.

Then the length is 3x.

Perimeter of a rectangle = 2(length + width)

200 = 2(3x + x)

200 = 6x + 2x

200 = 8x

200/8 = x

x = 25 cm.

Now, 

Length = 3(x)

= 3(25)

Length = 75 cm

Width = x 

Width = 25 cm

Problem 7 :

The Length of a rectangle is 10 cm. what is the width if the area is 60 cm² ?

Solution :

Given, Area =  60 cm², Length = 10 cm, and width = ?

Area of a rectangle = Length × width

60 = 10 × width

(60)/10 = width

width = 6 cm

Problem 8 :

The area of a rectangle is 48 cm². If its length is 12 cm, what is its width ?

Solution :

Given, Area =  48 cm², Length = 12 cm, and width = ?

Area of a rectangle = Length × width

48 = 12 × width

(48)/12 = width

width = 4 cm

Problem 9 :

The area of a rectangle is 27 cm². If its length is 9 cm, what is its width ?

Solution :

Given, Area =  27 cm², Length = 9 cm, and width = ?

Area of a rectangle = Length × width

27 = 9 × width

(27)/9 = width

width = 3 cm

Problem 10 :

Norman is a sunflower farmer. He uses a plot of land that is 3 km by 4.3 km. How much land does he use for his sunflowers?

Solution :

Norman uses the land which has dimensions of 3 km by 4.3 km.

The land is in a rectangular shape.

We find the area of a rectangular land.

Area of a rectangular land = Length × width

Length = 3 km, width = 4.3 km

Area = 3 × 4.3

Area = 12.9 km²

He used 12.9 km² of land for sunflowers.

Problem 11 :

Before soccer practice Allyson jogs around the field that measures 100 yards by 65 yards twice. How far will she jog ?

Solution :

Given, field that measures 100 yards by 65 yards.

we find the perimeter of the field.

Perimeter of a rectangle = 2(length + width)

Length = 100 yards, width = 65 yards

Perimeter = 2(100 + 65)

= 2(165)

Perimeter = 330 yards.

she runs twice,

= 2(330)

= 660 yards.

She will jog 660 yards.