Question
The perimeter of a square field is 16 cm more than the
perimeter of a rectangle. The length of the rectangle is 24 cm which is 150% 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, 150% of x = 24 x = 24 × 100/150 = 16 cm Perimeter of the rectangle = 2(length + width) = 2 × (24 + 16) = 80 cm Perimeter of the square = (80 + 16) = 96 cm The sides of the square = 96/4 = 24 cm The area of the square field without street = (24)2 sq. cm = 576 sq. cm The area of the square field with street = (24 + 20)2 sq. cm = 1936 sq. cm The area of the street = 1936 – 576 = 1360 sq. cm The total cost of constructing the street = 1360 × 25 = Rs. 34,000
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