Question
The perimeter of a square field is 16 cm more than the
perimeter of a rectangle. The length of the rectangle is 54 cm which is 225% 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. 25 per sq. cm?Solution
Let the width of the rectangle = x cm Then, 225% of x = 54 x = 54 × 100/225 = 24 cm Perimeter of the rectangle = 2(length + width) = 2 × (54 + 24) = 156 cm Perimeter of the square = (156 + 16) = 172 cm The sides of the square = 172/4 = 43 cm The area of the square field without street = (43)2 sq. cm = 1849 sq. cm The area of the square field with street = (43 + 20)2 sq. cm = 3969 sq. cm The area of the street = 3969 – 1849 = 2120 sq. cm The total cost of constructing the street = 2120 × 25 = Rs. 53,000
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