Answer:
1800 m²
Step-by-step 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
