Mathematics
The cost of enclosing a rectangular garden with a fence all around at the rate of ₹15 per metre is ₹5400. If the length of the garden is 100 m, find the area of the garden.
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Answer
Let ABCD be a rectangular garden.
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 = ₹ 15 per meter.
∴ Cost of enclosing fence all round the rectangular garden = ₹15(200 + 2x) = ₹(3000 + 30x).
Given cost = ₹5400
∴ 3000 + 30x = 5400
⇒ 30x = 5400 – 3000
⇒ x = = 80 m.
∴ Breadth of garden = 80 m.
So, the area of rectangular field = l × b
= 100 × 80
= 8000 m2.
Hence, the area of rectangular garden = 8000 m2.
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