A farmer wishes to start a 100 sq. rectangular vegetable garden. Since he has only 30 m barbed wire, he fences the sides of the rectangular garden letting his house compound wall act as the fourth side fence. Find the dimension of the garden.

Let ‘x’ and ‘y’ are the dimension of the vegetable garden.

Area of rectangle = Length × Width

x × y = 100

we are going to cover the barbed wire for fencing only. So, it must be the perimeter of vegetable garden. Usually perimeter always covers all the four side. Bute here we are going to cover only three sides, because one side of the vegetable garden will act as the compound wall.

x + x + y = 30

⇒ 2x + y = 30

⇒

⇒

⇒ 200 + y² = 30y

⇒ y² – 30y + 200 = 0

⇒ y² – 10y –20y + 200 = 0

⇒ y(y – 10) – 20(y – 10) = 0

⇒ (y – 10)(y – 20) =0

y – 10 = 0 or y – 20 = 0

y = 10 or y = 20

Now we are going to apply these values in to get the values of x.

If y = 10 if y = 20

x = 10 x = 5

Therefore, the required dimensions are 10m and 10m or 20m and 5m.