Maths-
General
Easy
Question
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 m2
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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