Question
The perimeter of a square field is 12 cm more than the
perimeter of a rectangle. The length of the rectangle is 40 cm which is 200% of its width. If a street of width 10 cm surrounds from outside the square, then find the total cost of constructing the street at the rate of Rs. 24 per sq. cm?Solution
Let the width of the rectangle = x cm Then, 200% of x = 40 x = 40 × 100/200 = 20 cm Perimeter of the rectangle = 2(length + width) = 2 × (40 + 20) = 120 cm Perimeter of the square = (120 + 12) = 132 cm The sides of the square = 132/4 = 33 cm The area of the square field without street = (33)2 sq. cm = 1089 sq. cm The area of the square field with street = (33 + 20)2 sq. cm = 2809 sq. cm The area of the street = 2809 – 1089 = 1720 sq. cm The total cost of constructing the street = 1720 × 24 = Rs. 41,280
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