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The length of a rectangular plot is 15 m more than its breadth. If the cost of fencing the plot at the rate of Rs. 16.50 per m is Rs. 4,950, then what is the length of the plot (in m)?

The length of a rectangular plot is 15 m more than its breadth. If the cost of fencing the plot at the rate of Rs. 16.50 per m is Rs. 4,950, then what is the length of the plot (in m)? Correct Answer 82.5

Given:

Length of rectangular plot is 15 m more than its breadth.

Rate of cost of fencing is Rs.16.50 per m.

Total cost of fencing is Rs.4,950.

Formula Used:

Perimeter of rectangle = 2(L + B)

Calculation:

Length of plot L = B + 15

Perimeter of plot = 2(L + B)

⇒ 2 {(B + 15 ) + B}

⇒ 2 (2B + 15)

⇒ 4B + 30

Now, the cost of fencing the plot at the rate of Rs.16.50 per m is Rs.4,950.

⇒ 16.50 × (4B + 30) = Rs.4,950

⇒ 66B + 495 = 4950

⇒ 66B = 4950 - 495

⇒ 66B = 4455

⇒ B = 4455/66 = 67.5

Length = B + 15 

⇒ 67.5 + 15 = 82.5

∴ Length of the rectangular plot = 82.5

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