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# The length of a rectangular field is twice its breadth. If the perimeter of the field is 180 m. Find its area. Also find the cost of fencing it at Rs.12 per metre.

## The correct answer is: Area of the given field is 1,800 m2 & cost of fencing it @ Rs. 12 per mt is Rs. 2,160

### Hint:-

i. Fencing refers to blocking or covering the boundaries of a land with fences i.e. wooden blocks to prevent livestock from getting away.

ii. Area of a rectangle = length × breadth

iii. Perimeter of a rectangle = 2 (length + breadth)

Step-by-step solution:-

Let the breadth of the given rectangular field be x m.

∴ breadth = x ........................................................................ (Equation i)

Now, from the given information-

Length = 2 × breadth

∴ Length = 2 × x = 2x …............................................................. (Equation ii)

Perimeter of the given field = 2 (length + breadth)

∴ Perimeter of the given field = 2 (2x + x) ................................. (From Equations i & ii)

∴ Perimeter of the given field = 2 × 3x

∴ Perimeter of the given field = 6x

∴ 180 = 6x .......................................... (From given information)

∴ 180 / 6 = x

∴ 30 = x

Substituting x = 30 in Equations i & ii,

breadth = x = 30 m ................................................................. (Equation iii)

length = 2x = 2 × 30 = 60 m ..................................................... (Equation iv)

∴ Area of the given field = length × breadth

∴ Area of the given field = 60 * 30

∴ Area of the given field = 1,800 m^{2}

Since fences are put on the boundaries of the field,

∴ cost of fencing the whole field (@ Rs. 12 per mt) = Perimeter of the field × rate

∴ cost of fencing the whole field (@ Rs. 12 per mt) = 180 × Rs. 12/ mt ........................ (From given information)

∴ cost of fencing the whole field (@ Rs. 12 per mt) = Rs. 2,160

Final Answer:-

∴ Area of the given field is 1,800 m2 & cost of fencing it @ Rs. 12 per mt is Rs. 2,160.

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