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2. You have 40 meters of fencing to enclose 4 sides of a rectangular garden.
a) Draw rectangle and label what you can
b) Let x represent the width of the garden. Write an expression for the length of the garden in terms of x.
c) Write function A(x) expressing the area of the garden.
d) Sketch and label graph.
e) Find the maximum of the garden area.

(help pls this is 8th grade maths and I'm learning quadratic equations/parabolas!!)​

Respuesta :

a) Here is a diagram of the rectangular garden with 4 sides enclosed by 40 meters of fencing:

```
+----x----+
| |
x x
| |
+----x----+
```

b) Let x represent the width of the garden. Since there are 4 sides, two sides will have length x and the other two sides will have length L. The total length of the fencing is given as 40 meters. So, we can write:

2x + 2L = 40

c) To find the expression for the length of the garden in terms of x, we can rearrange the equation from part b) as follows:

2L = 40 - 2x
L = 20 - x

d) Here is a sketch of the graph of the garden area:

```
^
| A(x)
|
+-----------------
0 x
```

e) To find the maximum area of the garden, we can use the area function A(x) expressed as:

A(x) = x(20 - x)

To find the maximum, we can take the derivative of A(x) with respect to x and set it equal to zero:

A'(x) = 20 - 2x = 0

Solving for x, we find:

20 - 2x = 0
2x = 20
x = 10

So, the maximum area of the garden can be found when the width is 10 meters.

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