There is a narrow rectangular plot, reserved for a school,in Mohali village. The length and breadth of the plot are in the ratio11:4. At the rate Rs 100 per metre it will cost the village panchayat Rs75000 to fence the plot. What are the dimensions of the plot?

1 answer

Let the length of the plot be \( 11x \) meters and the breadth be \( 4x \) meters, according to the given ratio of 11:4.

To find the perimeter \( P \) of the rectangular plot, we can use the formula:

\[ P = 2 \times (\text{Length} + \text{Breadth}) = 2 \times (11x + 4x) = 2 \times 15x = 30x \]

The cost to fence the plot is given as Rs 100 per meter, and the total cost is Rs 75000. Thus, we can relate the perimeter to the cost:

\[ \text{Total Cost} = \text{Perimeter} \times \text{Cost per meter} \]

Substituting the values we have:

\[ 75000 = 30x \times 100 \]

Now simplifying:

\[ 75000 = 3000x \]

Now, divide both sides by 3000 to find \( x \):

\[ x = \frac{75000}{3000} = 25 \]

Now we can find the dimensions of the plot.

  • Length \( = 11x = 11 \times 25 = 275 \) meters
  • Breadth \( = 4x = 4 \times 25 = 100 \) meters

Therefore, the dimensions of the plot are:

  • Length: 275 meters
  • Breadth: 100 meters