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What will be the cost of gardening 1 metre broad boundary around a rectangular plot having perimeter of 340 metres at the rate of Rs. 10 per square metre?
- a)Rs. 3,400/-
- b)Rs. 1700/-
- c)Rs. 3440/-
- d)Cannot be determined
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
What will be the cost of gardening 1 metre broad boundary around a rec...
(x+2) (y+2) - xy = Area of boundry
= xy +2x +2y + 4 -xy
=2x + 2y + 4 =344
then cost = 344 x 10 = 3440
Most Upvoted Answer
What will be the cost of gardening 1 metre broad boundary around a rec...
Calculation of Cost for Gardening 1 Metre Broad Boundary
Given:
Perimeter of the rectangular plot = 340 metres
Rate of gardening = Rs. 10 per square metre
Calculating the dimensions of the rectangular plot:
Let the length of the rectangular plot be 'l' metres and the breadth be 'b' metres.
Perimeter of a rectangle = 2(l + b)
Given, 2(l + b) = 340
l + b = 170
Since the boundary is 1 metre broad, the dimensions of the inner rectangle will be (l-2) and (b-2).
Therefore, the new length and breadth of the inner rectangle will be (l-2) and (b-2).
Calculating the area of the inner rectangle:
Area of the inner rectangle = (l-2)(b-2) square metres
Calculating the area of the boundary:
The area of the boundary = (l*b) - (l-2)(b-2) square metres
Calculating the cost of gardening:
Cost of gardening = Area of the boundary * Rate of gardening
Cost = [(l*b) - (l-2)(b-2)] * 10
Substitute l + b = 170 into the equation:
Cost = [(170-b)*b - (168)] * 10
Cost = (170b - b^2 - 1680) * 10
Cost = 10b^2 - 170b + 1680
To find the minimum cost, differentiate the cost function with respect to 'b' and equate it to zero.
d(Cost)/db = 20b - 170 = 0
b = 8.5
Substitute b = 8.5 into the cost function:
Cost = 10(8.5)^2 - 170(8.5) + 1680
Cost = 722.5
Therefore, the cost of gardening 1 metre broad boundary around the rectangular plot is Rs. 3440/-
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What will be the cost of gardening 1 metre broad boundary around a rectangular plot having perimeter of 340 metres at the rate of Rs. 10 per square metre?a)Rs. 3,400/- b)Rs. 1700/- c)Rs. 3440/-d)Cannot be determined e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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