The perimeter of a square field is 6 cm more than the perimeter of a rectangle. The length of the rectangle is 63 cm which is 175% 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. 22 per sq. cm?

Solution

Let the width of the rectangle = x cm Then, 175% of x = 63 x = 63 × 100/175 = 36 cm Perimeter of the rectangle = 2(length + width) = 2 × (63 + 36) = 198 cm Perimeter of the square = (198 + 36) = 204 cm The sides of the square = 204/4 = 51 cm The area of the square field without street = (51)² sq. cm = 2601 sq. cm The area of the square field with street = (51 + 20)² sq. cm = 5041 sq. cm The area of the street = 5041 – 2601 = 2440 sq. cm The total cost of constructing the street = 2440 × 22 = Rs. 53,680