Question

# The length and breadth of a rectangular piece of land are in the ratio 5:3. If the total cost of fencing at Rs.7 per metre is Rs.2800, find the area of the plot.

Hint – In order to solve this problem obtain the perimeter from the cost provided then with the help of perimeter obtain the length and breadth of the land and calculate the area doing this will solve our problem.

Ratio of length to breadth = 5:3

So, let length = 5x and breadth = 3x.

Cost of fencing = Rs.7 per meter
Total cost given is Rs.2800
Therefore, perimeter can be obtained by dividing the total cost with the cost of one meter.
So, the perimeter is $\dfrac{{2800}}{7}$ = 400 meter
We also know that the perimeter of a rectangle is 2 multiplied by length times breadth. So, 2(5x+3x) = 400
16x = 200
x = 25
So, length = 5(25) m=125m
And breadth =3(25) m = 75m
We know that the area of the rectangle is length time breadth.
So,
Area = 125×75 = 9375 ${{\text{m}}^{\text{2}}}$
Hence the answer is 9375 ${{\text{m}}^{\text{2}}}$.

Note – To solve this problem we need to know that the area of the rectangle is length time breadth and the perimeter of the rectangle is 2 multiplied by length times breadth. Here all we need to find is length and breadth to get the area. We have used the total cost and the cost per meter to find the perimeter and then with the help of perimeter we got the value of length and breadth.