Question
Download Solution PDFThe width of the path around a square field is 4.5 m and its area is 105.75 m2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The width of the path around a square field = 4.5 m
The area of the path = 105.75 m2
Formula used:
The perimeter of a square = 4 × Side
The area of a square = (Side)2
Calculation:
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 × (11/8) = 11/2 m
So, the total cost of fencing = (11/2) × 100 = Rs. 550
∴ The cost of fencing of the field is Rs. 550
Shortcut TrickIn such types of questions,
Area of path outside the Square is,
⇒ (2a + 2w)2w = 105.75
here, a is a side of a square and w is width of a square
⇒ (2a + 9)9 = 105.75
⇒ 2a + 9 = 11.75
⇒ 2a = 2.75
Perimeter of a square = 4a
⇒ 2 × 2a = 2 × 2.75 = 5.50
costing of fencing = 5.50 × 100 = 550
∴ The cost of fencing of the field is Rs. 550
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