Question

A rectangular field is twice as long as breath .A path of uniform widthh 2m is running inside the field . If the cost of constructing the path is rs40per sq m is ra 13760 find the area of the field

Answer 1

1800 m²

Explanation:

Since the cost of constructing the path at rs 40 per sq m is rs 13760, if A is the area of the path then we have

rate × area = cost

area = cost/rate = 13760/40 = 344 m²

Now, let L = length of rectangular field and B = breadth of rectangular field. So, its area is A'= LB. Given that L = 2B, A' = 2B × B = 2B².

Also, since the width of the path is 2 m, the inner field has dimensions L - 2 - 2 = L - 4 as length and B - 2 - 2 = B - 4 as breadth since we subtract 2 m from both ends of the each dimension.

So, the inner area is (L - 4)(B - 4) = (2B - 4)(B - 4) = 2B² - 8B - 4B + 16 = 2B² - 12B + 16.

The area of the rectangular field is thus the inner area plus the area of the uniform path

So, 2B² - 12B + 16 + 344

We equate this the the area of the rectangular field. So,

2B² - 12B + 16 + 344 = 2B²

- 12B + 16 + 344 = 2B² - 2B²

- 12B + 360 = 0

- 12B = -360

B = -360/-12

B = 30 m

Since the area of the field A' = 2B²,

A' = 2(30 m)²

= 2(900 m²)

= 1800 m²