Answer :

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 }.

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