Question

A man wants to protect a rectangular lawn in front of his house. The area of the lawn is 135 m² and he
has only 33 m barbed wire. He fences three sides of the lawn with barbed wire and the fourth side ir
protected by the compound wall of his house. If the barbed wire is just sufficient for fencing of the
three sides, find the dimensions of the lawn.​

Answer 1

Answer:

l×b=100 (1)

Wire used for fencing three sides or Perimeter of 3 sides of garden =30m

b+l+b=30

⇒2b+l=30 (2)

Putting value of l from (2) in (1), we get

b(30−2b)=100

⇒2b

2

−30b+100=0

⇒b

2

−15b+50=0

On solving the quadratic equation by splitting the middle term, we get

b=5,10

If b=10, then we get l=10, which is not possible, as it is a rectangular garden.

so we take b=5⇒l=20

So, the width of the rectangular garden is 5m

Answer 2

A man wants to protect a rectangular lawn in front of his house. The area of the lawn is 135 m² and he

has only 33 m barbed wire. He fences three sides of the lawn with barbed wire and the fourth side ir

protected by the compound wall of his house. If the barbed wire is just sufficient for fencing of the

three sides, find the dimensions of the lawn.​