Question

There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate ₹100 per meter it will cost the village panchayat ₹75,000 to fence the plot. What are the dimensions of the plot?

• A. 270 m, 100 m
• B. 275 m, 100 m
• C. 275 m, 105 m
• D. 270 m, 105 m

Answer 1

The correct option is B 275 m, 100 m

Let the length and breadth of the rectangular plot be $11x$ and $4x$ respectively.
Perimeter of the plot
$=\frac{Totalcost}{Costof1meter}=\frac{75000}{100}=750m$
We know that the perimeter of rectangle = 2(length + breadth)
Therefore, according to the question,
$750=2(11x+4x)$
$\Rightarrow 750=2\times 15x$
$\Rightarrow 750=30x$
$\Rightarrow 30x=750$
$\Rightarrow x=\frac{750}{30}=25$
Hence, the length of rectangular plot = $11\times 25=275m$ and the breadth of rectangular plot = $4\times 25=100m$
Hence, the dimensions of the plot are 275 m and 100 m respectively.