A farmer wishes to grow a 100 m ²rectangular vegetable garden.Since he has with him only 30 m barbed wire, he fences three sides of therectangular garden letting compound wall of his house act as the fourthside-fence. Find the dimensions of his garden.
[Hint: If the length of one side is x metres, the other side will be (30- 2x) m. Therefore, x(30 - 2x) = 100]

Let the length of one side is x m.
Then other side will be(30 - 2x) m.
Therefore, x(30 - 2x) = 100
30x - 2x ² = 100
-2x ² + 30x – 100 = 0
x ² – 15x + 50 = 0
x ² – 10x – 5x + 50 = 0
x(x – 10) – 5(x – 10) = 0
(x – 5)(x – 10) = 0
(x – 5) = 0 or (x – 10) = 0
x = 5 or x = 10
If one side is 5 m then the other side is 20 m, so the three side of the fence would be 25 m.
If one side is 10 m then the other side is 10 m, so the three side of the fence would be 30 m.
Since the fence wire is 30 m we consider the dimensions of his garden is 10 m and 10 m.
Checking:
a) Area of the rectangular vegetable garden = 10 m × 10 m = 100 m ² .