Mathematics
The cost of enclosing a rectangular garden with a fence all around at the rate of ₹ 150 per metre is ₹ 54,000. If the length of the garden is 100 m, find the area of the garden.
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Answer
Given,
Length = 100 m.
Let breadth = x meters.
By formula,
Perimeter of rectangle = 2(l + b)
Substituting the values we get,
Perimeter of rectangular garden = 2(100 + x) = (200 + 2x) m.
Given,
Cost of enclosing fence = ₹ 150 per meter.
∴ Cost of enclosing fence all round the rectangular garden = ₹150(200 + 2x) = ₹(30,000 + 300x).
Given, total cost of fencing = ₹ 54,000
∴ 30,000 + 300x = 54,000
⇒ 300x = 54,000 – 30,000
⇒ 300x = 24,000
⇒ x =
⇒ x = 80 m.
∴ Breadth of garden = 80 m.
So, the area of rectangular garden = length × breadth
= 100 × 80
= 8000 m2.
Hence, the area of rectangular garden = 8000 m2.
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