Question

Mathematics - Perimeter and Area
The length and breadth of a rectangular piece of land are, in the ratio 5:2. If the total cost of fencing it at Rs. 12.5
per meter is Rs. 25000, find its length and breadth.​

Answer 1

Answer: Length = 714.25 metres, Breadth = 285.7 metres. (approximately)

Step by step explanation:

Given:

Ratio of length and breadth of rectangular piece of land = 5 : 2.

Cost of fencing per m: Rs. 12.5 per m.

Total cost: Rs. 25,000.

To find: Length and breadth.

Solution:

Total cost of fencing / Rate per m = Perimeter

.°. 25000/12.5 = Perimeter

Perimeter = 2000 metres

Now, let the length be 5x and breadth be 2x.

Perimeter of rectangular piece of land= 2( length + breadth)

2000 = 2 ( 5x + 2x )

2000 = 2 × 7x

1000 = 7x

x = 142.85 metres. (approx.)

Length = 5x = 5 × 142.85 = 714.25 metres (approx.)

Breadth = 2x = 2 × 142.85 = 285.70 metres (approx.)

Thus, It's length and breadth are 714.25 metres and 285.7 metres (approx.) respectively.

Answer 2

Answer:

Ratio of length to breadth = 5:2 ( given)

So, If length of the field = 5x m , breadth = 2x m

So, the total length of fencing ( perimeter of the field) = 10x + 4x = 14x m . . . . .(1)

Since Rs 12.5 is the cost of 1 m fencing

=> Rs25,000, spent for=(25000/12.5) m fencing

= (25000 x 10 ) / 125

= 200 x 10

= 2000 m . . . . .(2)

By (1)&(2)

14x = 2000

=> x = 2000/14 = 1000/7

=>lengthof the field= 5x=5*1000/7 = 5000/7 m

& breadth = 2x = 2*1000/7= 2000/7 m