Question

The length and breadth of a rectangular plot are in ratio 11:4. The cost of fencing the plot with wire is rupees 18000 at the rate of rupees 100 per metre. Find the dimens of the plot using x. ( one variable )

Answer 1

Solution:

Given Information:

Length : Breadth = 11 : 4

Cost of Fencing = Rs. 15000 ( Rs. 100 per m² )

To Find:

Dimensions of the Plot

Illustration:

Let the ratio of length and breadth be 11x : 4x respectively.

So Fencing refers to Perimeter of the plot

So Perimeter = 2 ( l + b ) as it is a rectangular plot.

Also we know that,

Perimeter × Cost per m² = Total Cost

=> Perimeter × 100 = 15000

=> Perimeter = 15000 / 100 = 150 m

Hence the perimeter is 150 m.

So Perimeter of Rectangular Plot = 2 ( l + b )

We know 'l' = 11 x and 'b' = 4x

So 2 ( 11x + 4x ) = 150

=> 2 ( 15 x ) = 150

=> 30 x = 150

=> x = 150 / 30

=> x = 5

Hence the value of 'x' is 5.

So Length = 11 x = 11 × 5 = 55 m

Breadth = 4 x = 4 × 5 = 20 m

Hence the dimensions are 55 m and 22 m.

Hope my answer helped !