a man decides to create a vegetable garden. He buys 100m of wire netting to fence off a rectangular area from the kangaroos. There is already an existing fence on one side of the rectangle, so the 100m of wire netting is for the other 3 sides.If x is the width of the rectangular garden, write an expression for the length of the garden in terms of x.

It depends on what you are calling the width. Make your diagram...

If w is the width of the garden parallel to the existing fence, then there are two other sides of length y. So,
w+2y = 100
y = (100-w)/2

If w is one of the two sides perpendicular to the fence, then there is only one other side, with length y. So,
2w+y = 100
y = 100-2w

To find the expression of the length of the garden in terms of x, let's break down the problem.

The garden has four sides: three sides need to be fenced off by the wire netting, while one side is already fenced. So, the wire netting will be used to fence the remaining three sides.

Let's denote the width of the rectangular garden as x meters. Since the width should be fenced on all sides, we need to use 2x meters of the wire netting for the width.

Now, let's consider the length of the garden. Since one side of the garden is already fenced, we only need to fence the other two remaining sides. Let's call the length of the garden y meters.

Therefore, we need 2x meters of wire netting for the width and y meters of wire netting for the length. The total length of wire netting required is given by the equation:

Length of wire netting = 2x + y

Since you are looking for the expression for the length of the garden in terms of x, we can rewrite that equation as:

y = Length of wire netting - 2x

So, the expression for the length of the garden in terms of x is:

y = 100 - 2x

Here, the length of the garden (y) is equal to 100 minus twice the width of the garden (x).