Page 235 - ICSE Math 7

Example 1: A rectangular plot is 50 m long and 30 m wide. Find the:
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(a) area of the plot. (b) cost of the plot, if 1 m costs ` 1,000.
Solution: (a) Area of rectangle = length × breadth
Length of the rectangular plot = 50 m
Breadth of the rectangular plot = 30 m
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∴ area of rectangular plot = 50 m × 30 m = 1,500 m .
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(b) Cost of rectangular plot = Cost of 1 m of the plot × area of the plot
= ` 1,000 × 1,500 = ` 15,00,000
∴ cost of plot is ` 15,00,000.
Example 2: The perimeter of a rectangular sheet is 100 cm. If its
length is 40 cm, find its breadth. Also find the area of Try These
the rectangle. 1. Find the area of a square
Solution: Perimeter of rectangular sheet = 100 cm park whose perimeter is
220 m.
Length (l) of the sheet = 40 cm 2. Find the breadth of a
Perimeter = 2(l + b) = 100 cm rectangular plot of land, if
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⇒ 2(40 + b) = 100 its area is 180 m and the
⇒ 40 + b = 50 length is 20 m. Also find its
perimeter.
⇒ b = 10 cm
Area of the sheet = l × b = 40 cm × 10 cm = 400 cm 2

Example 3: 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
2
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Area of the square park = (side) = (80 m) = 6,400 m 2
Since, area of the rectangular park = area of the square park
⇒ l × b = 6,400 m 2
⇒ 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 4: 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) cm = 2 × 60 cm = 120 cm
Perimeter of the square = 4 × side = 120 cm
120
∴ side of square = 4 cm = 30 cm

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Area of square = (side) = 30 cm × 30 cm = 900 cm 2
Area of rectangle = l × b = 40 cm × 20 cm = 800 cm 2
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Difference in area = 900 cm – 800 cm = 100 cm 2
Thus, the square shape encloses more area.

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