Bimal wishes to start a 200 metre square rectangular garden. Since he has only 50 m barbed wire, he fences three sides of the garden letting his house compound wall act as one of the longer sides of the garden. Find the dimensions of the garden.

Asked by khushdab | 1st Apr, 2020, 04:48: PM

Expert Answer:

Let l and b be the length and breadth of the garden
Only thre sides of the garden are fenced.
l+2b=50 ... (i)
Area of the garden is 200 m2
lb=200
Using (i), we have
(50 - 2b)b=200
2b2 - 50b + 200 = 0
b2 - 25b + 100 = 0
b2 - 20b - 5b + 100 = 0
b(b - 20) - 5(b - 20) = 0
(b - 20)(b-5) = 0
b = 20  or  b = 5
When b = 20, l = 50 - 40 = 10
When b = 5, l = 50 - 10 = 40
Hence, the sides of the garden are 20 and 10 or 5 and 40.

Answered by Renu Varma | 1st Apr, 2020, 05:57: PM

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