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Question

A farmer wishes to grow a 100m2 rectangular vegetable garden. Since he has with the only 30m barbed wire, he fences three sides of the rectangular garden letting the compound wall of his house act as the fourth side – fence. Find the dimensions of his garden.


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Solution

Step 1: Let's find the value of each sides of the fence in the garden.

Let the length of one side be x metres

Let the length of the other side be y metres

Here one side is a compound wall and 30 m wire is used for fencing.

x+y+x=30

y=302x

Area of the vegetable garden =100m2

xy=100

x(302x)=100

30x2x2=100

15xx2=50

x215x+50=0

x210x5x+50=0

x(x10)5(x10)=0

(x10x)(x+5)=0

x=5and10

Step 2: Let's find the dimensions of the garden.

When x=5,

y=30-(2×5)

y=3010

y=20

When x=10,

y=30-(2×10)

y=3020

y=10

Therefore, the dimensions of his garden will be 5m×20m or 10m×10m


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