Question
The perimeter of a square field is 16 cm more than the
perimeter of a rectangle. The length of the rectangle is 72 cm which is 300% 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. 20 per sq. cm?Solution
Let the width of the rectangle = x cm Then, 300% of x = 72 x = 72 × 100/300 = 24 cm Perimeter of the rectangle = 2(length + width) = 2 × (72 + 24) = 192 cm Perimeter of the square = (192 + 16) = 208 cm The sides of the square = 208/4 = 52 cm The area of the square field without street = (52)2 sq. cm = 2704 sq. cm The area of the square field with street = (52 + 20)2 sq. cm = 5184 sq. cm The area of the street = 5184 – 2704 = 2480 sq. cm The total cost of constructing the street = 2480 × 20 = Rs. 49,600
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