Question

13. 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:

Let the length of one side be x meters and other side be y meters. Then,

⇒ x+y+x=30 ----- ( 1 ) [ Given ]

∴ y=30−2x ----- ( 2 )

⇒ Area of the vegetable garden =100m

2

⇒ xy=100

⇒ x(30−2x)=100 [ From ( 2 ) ]

⇒ 30x−2x

2

=100

⇒ 15x−x

2

=50

⇒ x

2

−15x+50=0

⇒ x

2

−10x−5x+50=0

⇒ (x−10)(x−5)=0

⇒ x=5,10

When x=5, we have

⇒ y=30−2×5=20

When x=10, we have

⇒ y=30−2×10=10

∴ The dimensions of rectangular garden are 20m,5m or 10m,10m