Question
The perimeter of a square field is 20 cm more than the
perimeter of a rectangle. The length of the rectangle is 56 cm which is 400% 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. 30 per sq. cm?Solution
Let the width of the rectangle = x cm Then, 400% of x = 56 x = 56 × 100/400 = 14 cm Perimeter of the rectangle = 2(length + width) = 2 × (56 + 14) = 140 cm Perimeter40 of the square = (140 + 20) = 160 cm The sides of the square = 160/4 = 40 cm The area of the square field without street = (40)2 sq. cm = 1600 sq. cm The area of the square field with street = (40 + 20)2 sq. cm = 3600 sq. cm The area of the street = 3600 – 1600 = 2000 sq. cm The total cost of constructing the street = 2000 × 30 = Rs. 60,000
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