Question

There is a narrow rectangular plot. The length and breadth of the plot are in the ratio of 11:4. At the rate of Rs. 100 per meter it will cost the village panchayat Rs. 75000 to fence the plot. What are the dimensions of the plot?​

Answer 1

$\underline{\huge{Solution:-}}$

let the common ratio be x

The length and breadth of a rectangular plot be 11x and 4x.

We know that perimeter of rectangal =${\boxed{\sf{ 2(length + breadth)}}}$

Therefore, the perimeter of the plot here is:

$\sf\large{= 2(11x + 4x)}$

$\sf\large{= 2(15x)}$

$\sf\large{= 30x}$

Given that Cost of fencing the plot at the rate of rs.100 per metre is 75000.

$\sf\large{➪ 100 × Perimeter = 75000}$

$\sf\large{➪100 × 30x = 75000}$

$\sf\large{➪ 3000x = 75000}$

$\sf\large{➪x = 25}$

So,

$\bf{Length\:of\:rectangular\:plot = 11x = 275m}$

$\bf{Breadth\:of\:rectangular\:plot= 4x = 100m}$

Hence, the dimensions of the rectangular plot are 275m and 100m respectively.

Answer 2

$\large{ \underline{ \overline{ \mid{ \rm{ \red{Given}} \mid}}}}$

• the ratio of length and breadth of the plot is 11:4.
• the rate of fencing per meter is Rs. 100.
• the total amount paid by the village panchayat to fence the plot is Rs. 75000.

$\large{ \underline{ \overline{ \mid{ \rm{ \red{To\:Find}} \mid}}}}$

• the dimensions of the plot.

From the question, we get the ratio of the plot as,

$\large{\sf{\frac{Length}{Breadth}=\frac{11}{4}}}$

Now,we'll try to find out the perimeter of the rectangle from the total cost of fencing.So,the total perimeter of the plot is given as,

$\large{\sf{\frac{Total\:cost\:of\:fencing}{Cost\:of\:1\:m\:of\:fencing}}}$

$\large{\sf{=\frac{75000}{100}}}$

$\large{\sf{=750\:\:m}}$

We know that the perimeter of a rectangle is givem by 2(l+b) and we have the perimeter of the rectangle as 750 m.

So, A.T.Q

$2(l + b) = 750$

But the length and breadth is given as the ratio of 11:4.So,by equating them we get,

$2(11x + 4x) = 750$

$→2 \times 15x = 750$

$→30x = 750$

$→x = \frac{750}{30}$

$→x = 25$

So, we get the length of the given rectangle as (11×25)=275 m and bredth as (4×25)=100 m.

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$\large{ \underline{ \overline{ \mid{ \rm{ \red{Length →275\:\:m}} \mid}}}}$

$\large{ \underline{ \overline{ \mid{ \rm{ \red{Breadth →100\:\:m}} \mid}}}}$

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