Page 237 - Start Up Mathematics_7

Example 3: The perimeter of a rectangular sheet is 100 cm. If its length is 40 cm, find its breadth.

Also find the area of the rectangle.
Solution: Perimeter of rectangular sheet = 100 cm
Length (l) of the sheet = 40 cm

Perimeter = 2(l + b) = 100 cm
⇒ 2(40 + b) = 100

⇒ 40 + b = 50
⇒ b = 10 cm

Area = l × b = 40 cm × 10 cm = 400 cm 2
2
Example 4: Find the breadth of a rectangular plot of land, if its area is 180 m and the length is
20 m. Also find its perimeter.

Solution: Area of the rectangular plot = 180 m 2
Length of the plot = 20 m

2
Breadth of the plot = Area ÷ length = 180 m ÷ 20 m = 180 = 9 m
20
Perimeter of the plot = 2 × (l + b) = 2 × (20 + 9) = 2 × 29 = 58 m
Example 5: The area of a square park is same as that of a rectangular park. If the side of the
square park is 80 m and the length of the rectangular park is 100 m, find the breadth
of the rectangular park.
Solution: Side of the square park = 80 m 80 m

2
2
Area of the square park = (side) = 80 = 6,400 m 2
Since, area of the rectangular park = Area of the square park b
⇒ l × b = 6,400 m 2 100 m
⇒ 100 × b = 6,400 ( l = 100 m)

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∴ breadth (b) of the park = Area ÷ Length = 6,400 m ÷ 100 m = 64 m
Example 6: A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 20 cm. If the
same wire is re-bent to form a square, what will be the measure of its side? Also

find which shape will enclose more area, and by how much?
Solution: Length of the rectangle = 40 cm
Breadth of the rectangle = 20 cm

Perimeter of the wire = 2 × (l + b) = 2 × (40 + 20) = 2 × 60 = 120 cm
Perimeter of the square = 4 × side = 120 cm
120
∴ side of square = 4 = 30 cm
2
Area of square = (side) = 30 × 30 = 900 cm 2
Area of rectangle = l × b = 40 × 20 = 800 cm 2

Thus, the square shape encloses more area.
2
Difference in area = 900 – 800 = 100 cm .

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