Chapter 9: Perimeter and Area

Q1Written answer

The length and breadth of a rectangular piece of land are 500 m and 300 m, respectively. Find

(i) Its area (ii) the cost of the land, if 1 m² of the land costs ₹ 10,000.

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Solution:-

From the question, it is given that

Length of the rectangular piece of land = 500 m

Breadth of the rectangular piece of land = 300 m

Then,

(i) Area of rectangle = Length × Breadth

= 500 × 300

= 150000 m²

(ii) Cost of the land for 1 m² = ₹ 10000

Cost of the land for 150000 m² = 10000 × 150000

= ₹ 1500000000

Q2Written answer

Find the area of a square park whose perimeter is 320m.

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Solution:-

From the question, it is given that

Perimeter of the square park = 320 m

4 × Length of the side of park = 320 m

Then,

Length of the side of the park = 320/4

= 80 m

So, the area of the square park = (Length of the side of the park)²

= 80²

= 6400 m²

Q3Written answer

Find the breadth of a rectangular plot of land if its area is 440 m² and the length is 22 m. Also, find its perimeter.

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Solution:-

From the question, it is given that

Area of the rectangular plot = 440 m²

Length of the rectangular plot = 22 m

We know that,

Area of the rectangle = Length × Breadth

440 = 22 × Breadth

Breadth = 440/22

Breadth = 20 m

Then,

Perimeter of the rectangle = 2(Length + Breadth)

= 2 (22 + 20)

= 2(42)

= 84 m

∴ Perimeter of the rectangular plot is 84 m.

Q4Written answer

The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth.

Also, find the area.

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Solution:-

From the question, it is given that

Perimeter of the rectangular sheet = 100 cm

Length of the rectangular sheet = 35 cm

We know that,

Perimeter of the rectangle = 2 (Length + Breadth)

100 = 2 (35 + Breadth)

(100/2) = 35 + Breadth

50 – 35 = Breadth

Breadth = 15 cm

Then,

Area of the rectangle = Length × Breadth

= 35 × 15

= 525 cm²

∴ Area of the rectangular sheet is 525 cm²

Q5Written answer

The area of a square park is the same as that of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

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Solution:-

From the question, it is given that

The area of a square park is the same as that of a rectangular park.

Side of the square park = 60 m

Length of the rectangular park = 90 m

We know that,

Area of the square park = (One of the sides of the square)²

= 60²

= 3600 m²

Area of the rectangular park = 3600 m² … [∵ given]

Length × Breadth = 3600

90 × Breadth = 3600

Breadth = 3600/90

Breadth = 40 m

Q6Written answer

A wire is in the shape of a rectangle. Its length is 40 cm, and its breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side?

Also, find which shape encloses more area.

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Solution:-

By reading the question, we can conclude that the perimeter of the square is the same as the perimeter of the rectangle.

From the question, it is given that

Length of the rectangle = 40 cm

Breadth of the square = 22 cm

Then,

Perimeter of the rectangle = Perimeter of the Square

2 (Length + Breadth) = 4 × side

2 (40 + 22) = 4 × side

2 (62) = 4 × side

124 = 4 × side

Side = 124/4

Side = 31 cm

So, the area of the rectangle = (Length × Breadth)

= 40 × 22

= 880 cm²

Area of square = side²

= 31²

= 31 × 31

= 961 cm²

∴ Square-shaped wire encloses more area.

Q7Written answer

The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30 cm, find its length. Also, find the area of the rectangle.

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Solution:-

From the question, it is given that

Perimeter of the rectangle = 130 cm

Breadth of the rectangle = 30

We know that

Perimeter of rectangle = 2 (Length + Breadth)

130 = 2 (length + 30)

130/2 = length + 30

Length + 30 = 65

Length = 65 – 30

Length = 35 cm

Then,

Area of the rectangle = Length × Breadth

= 35 × 30

= 1050 cm²

Q8Written answer

A door of length 2 m and breadth 1 m is fitted in a wall. The length of the wall is 4.5 m, and the breadth is 3.6 m (Fig). Find the cost of whitewashing the wall if the rate of whitewashing the wall is ₹ 20 per m².

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Worked solution

Solution:-

From the question, it is given that

Length of the door = 2 m

Breadth of the door = 1 m

Length of the wall = 4.5 m

Breadth of the wall = 3.6 m

Then,

Area of the door = Length × Breadth

= 2 × 1

= 2 m²

Area of the wall = Length × Breadth

= 4.5 × 3.6

= 16.2 m²

So, area to be whitewashed = 16.2 – 2 = 14.2 m²

Cost of whitewashing 1 m² area = ₹ 20

Hence, the cost of whitewashing 14.2 m² area = 14.2 × 20

= ₹ 284

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Exercise 11.1