The area of a rectangular field is 1008 m². Its shorter side is 1/8 of the sum…

Solution

Let the longer side of the rectangular field be l metres and the shorter side be b metres.

Given:

Area of the rectangle = 1008 m²
Shorter side is 1/8 of the sum of the longer side and a diagonal.

Therefore,

b = (l + d)/8

where d is the diagonal of the rectangle.

Rearranging,

8b = l + d

d = 8b − l

Using the Pythagorean theorem for a rectangle:

d² = l² + b²

Substituting d = 8b − l,

(8b − l)² = l² + b²

64b² − 16bl + l² = l² + b²

64b² − 16bl = b²

63b² − 16bl = 0

b(63b − 16l) = 0

Since b ≠ 0,

63b = 16l

l = (63/16)b

Using the area of the rectangle,

l × b = 1008

(63/16)b × b = 1008

63b² = 16128

b² = 256

b = 16 m

Hence,

l = (63/16) × 16 = 63 m

Perimeter of the field

= 2(l + b)

= 2(63 + 16)

= 2 × 79

= 158 m

Cost of fencing

= Perimeter × Rate

= 158 × 24

= ₹3792

Therefore, the cost of fencing the field is ₹3792.

Answer: C) 3792