1. The Length and the 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.
Solution:
(i) Its area
Given,
Length of the rectangular piece of land = 500 m
Breadth of the rectangular piece of land = 300 m
Now,
Area of rectangle = Length × Breadth
= 500 × 300
= 150000 m2
(ii) the cost of the land, if 1 m2 of the land costs ₹ 10,000.
Cost of the land for 1 m2 = ₹ 10000
Cost of the land for 150000 m2 = 10000 × 150000
= ₹ 1500000000
2. Find the area of a square park whose perimeter is 320m.
Solution:
Given,
The perimeter of the square park = 320 m
Then,
4 × Length of the side of the park = 320 m
Now,
Length of the side of the park = 320/4
= 80 m
Hence, the Area of the square park = (length of the side of the park)2
= 802
= 6400 m2
3. 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.
Solution:
Given,
Area of the rectangular plot = 440 m2
Length of the rectangular plot = 22 m
We know,
Area of the rectangle = Length × Breadth
440 = 22 × Breadth
Breadth = 440/22
Breadth = 20 m
Now,
Perimeter of the rectangle = 2(Length + Breadth)
= 2 (22 + 20)
= 2(42)
= 84 m
Hence, Perimeter of the rectangular plot is 84 m.
4. The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.
Solution:
Given,
Perimeter of the rectangular sheet = 100 cm
Length of the rectangular sheet = 35 cm
We know,
Perimeter of the rectangle = 2 (Length + Breadth)
100 = 2 (35 + Breadth)
(100/2) = 35 + Breadth
50 – 35 = Breadth
Breadth = 15 cm
Now,
Area of the rectangle = Length × Breadth
= 35 × 15
= 525 cm2
Hence, Area of the rectangular sheet is 525 cm2
5. The area of a square park is the same as 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.
Solution:
Given,
Area of a square park is the same as of a rectangular park.
Side of the square park = 60 m
Length of the rectangular park = 90 m
We know,
Area of the square park = (side)2
= 602
= 3600 m2
Given, Area of the rectangular park = 3600 m2
Length × Breadth = 3600
90 × Breadth = 3600
Breadth = 3600/90 Breadth = 40 m
6. A wire is in the shape of a rectangle. Its length is 40 cm and 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?
Solution:
According to the question, we can conclude that the perimeter of the square is the same as the perimeter of the rectangle.
Given,
Length of the rectangle = 40 cm
Breadth of the square = 22 cm
So,
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
Now, Area of the rectangle = (Length × Breadth)
= 40 × 22
= 880 cm2
Area of square = side2
= 312
= 961 cm2
Hence, Square shaped wire encloses more area.
7. 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.
Solution:
Given,
Perimeter of the rectangle = 130 cm
Breadth of the rectangle = 30
We know,
Perimeter of rectangle = 2 (Length + Breadth)
130 = 2 (length + 30)
130/2 = length + 30
Length + 30 = 65
Length = 65 – 30
Length = 35 cm
Now,
Area of the rectangle = Length × Breadth
= 35 × 30
= 1050 cm2
8. 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 white washing the wall, if the rate of white washing the wall is ₹ 20 per m2.
Solution:
Given,
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
Now,
Area of the door = Length × Breadth
= 2 × 1
= 2 m2
Area of the wall = Length × Breadth
= 4.5 × 3.6
= 16.2 m2
Then, Area to be white washed = 16.2 – 2 = 14.2 m2
Cost of white washing 1 m2 area = ₹ 20
Hence cost of whit washing 14.2 m2 area = 14.2 × 20
= ₹ 284
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