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Question

A person wishes to make a 100 sq. m rectangular garden. Since he has only 30 m barbed wire for fencing, he fences only three sides letting the house wall act as the fourth side. The width of the garden is

A
10 m
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B
5 m
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C
50 m
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D
100 m
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Solution

The correct option is A 5 m

Area of the garden =100m2

Or, l×b=100

Or, l=100b

Given that, the garden is fenced on three sides.

Hence, length of fencing =2b+l=30

200l+l=30

l230l+200=0

l220l10l+200=0

l(l20)10(l20)=0

(l20)(l10)=0

Hence, l=20or10

Or, b=10020=5or10010=10

Since, the garden is in the shape of a rectangle, the length and breadth cannot be equal.

Therefore, the length and the breadth of the garden are 20 m and 5 m respectively.

Hence, the width of the rectangular garden is 5 m.


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