A gardener is putting a fence along the edge of his garden. If he has 20 m of fence , what is the largest area he can enclose? How can a graph solve the problem? What quadratic equation represents the area of the garden?

Not clear about your question.

Does he put a fence around a rectangular garden, on all 4 sides?
Often , for this kind of question , one side is not neede. Please clarify .

It's a rectangular garden,on all 4 sides,and how does a graph solve the problem?

It's a rectangular garden and the fence is on 4 sides,my question is how does graph help

To find the largest area the gardener can enclose with a given length of fence, we can start by understanding the shape of the garden that will maximize the area. In this case, the shape is a rectangle since the gardener is putting a fence along the edge of the garden.

Let's assume the length of the garden is L and the width is W. Since the garden is rectangular, we know that the perimeter of the garden (which requires the fence) is twice the length plus twice the width: Perimeter = 2L + 2W.

Given that the gardener has 20 m of fence, we can set up an equation: 2L + 2W = 20.

To solve this equation, we need to express one of the variables (L or W) in terms of the other, so we can find the maximum area. Let's solve for L:

2L = 20 - 2W
L = 10 - W.

Now we have an equation for L in terms of W, and we know that the area of a rectangle is A = L * W. So, we can substitute L = 10 - W into the area equation:

A = (10 - W) * W.

This equation represents the area of the garden as a function of its width, W. To find the maximum area, we can graph this quadratic equation.

To graph the equation, we can plot points for different values of W and calculate the corresponding A. By observing the graph, we can find the maximum point on the curve, which will give us the width and length that maximize the area.

Once we find the value of W that corresponds to the maximum area, we can substitute it back into the equation L = 10 - W to find the length L. This will tell us the dimensions of the garden that enclose the largest possible area given the 20 meters of fence.

Therefore, the quadratic equation that represents the area of the garden is A = (10 - W) * W.