The width of the path around a square field is 4.5 m and its area is 105.75 . Find the cost of fencing the path at the rate ofRs100 per metre.
This questions was previously asked in
SSC CGL 11th April 2022 Shift-2
Explanation:
Correct option: 1
Solution:The perimeter of a square = 4 x Side
The area of a square = (Side)2
Let, each side of the field = x
Then, each side with the path = x + 4.5 +4.5 = x + 9
So, (x+9)2 - x2 = 105.75
⇒ x2 + 18x + 81 - x2 = 105.75
⇒ 18x+81 = 105.75
⇒ 18x = 105.75 81 = 24.75
⇒x= 24.75/18 = 11/8
.. Each side of the square field = 11/8 m
The perimterer = 4 x (11/8) = 11/2 m
So, the total cost of fencing = (11/2) x 100 = Rs. 550
Hence the cost of fencing of the field is Rs. 550
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By: santosh