The perimeter of a square playground is 8 cm more than the perimeter of a rectangle. The length of the rectangle is 63 cm which is 300% of its width. If a path of a width of 10 cm surrounds from outside the square, then find the total cost of constructing the path at the rate of Rs. 25 per sq. cm?
1. 62,000
2. 44,000
3. 54,000
4. 52,000
5. 48,000
1. 62,000
2. 44,000
3. 54,000
4. 52,000
5. 48,000
Correct Answer – Option 3 : 54,000
Calculation:
Let the width of the rectangle = x cm
Then, 300% of x = 63
⇒ 300/100 × x = 63
⇒ x = 63 × 100/300
⇒ x = 21
Perimeter of the rectangle = 2(length + width)
⇒ 2(63 + 21)
⇒ 168 cm
∴ Perimeter of the square = (168 + 8) = 176 cm
The side of the square = 176/4
⇒ 44
The area of the square playground without path = (44)2 sq. cm
⇒ 1936 sq. cm
The area of the square playground with path = (44 + 20)2 sq. cm
⇒ 4096 sq. cm
The area of the path = 4096 – 1936
⇒ 2160 sq. cm
The total cost of constructing the path = 2160 × 25
⇒ 54000
The total cost of constructing the path at the rate of Rs. 25 per sq. cm is 54,000.