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 Rs.100 per metre it will cost the village panchayat Rs.75000 to fence the plot. What are the dimensions of the plot?​

Answer 1

Given:-

• The length and breadth of the plot are in the ratio 11:4.
• At the rate Rs.100 per metre it will cost the village panchayat Rs.75000 to fence the plot.

⠀

To find:-

• dimensions of the plot.

⠀

Solution:-

Let,

• the ratio of their sides be x.

Then,

→ Perimeter = 2(l+b)

→ Perimeter = 2(11x+4x)

→ Perimeter = 2(15x)

→ Perimeter = 30x

☆ Since it's giveb that the cost of one meter is 100 and total cost of fencing is 75,000, we will find the perimeter with these given terms.

★Perimeter × per metre = Total cost

→ 30x × 100 = 75,000

→ 3000x = 75,000

→ x = 75,000/3000

→ x = 25

Dimensions of the plot,

→ Length = 11x

→ 11×25

→ 275

⠀

→ Breadth = 4x

→ 4 × 25

→ 100

Answer 2

Let the length and breadth's common ratio: x in metre

∴ Length :11x and Breadth :4x

Perimeter ⇒2(l+b)

=2(11x+4x)=30x

As per the question:

Cost of fencing plot at rate of Rs.100 per meter is Rs.75000

∴100× Perimeter =75000

3000x=75000

x=25

Length =11×x=11×25=275 m

Breadth =4x,=4×25=100 m