what is the largest are of rectangular area that can be enclosed in sixteen meter fence

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I am sure that I have answered this one recently

Let the width of the rectangle = w and the height = h

2w+2h=16 or

w=8-h

the area=wh or

area = (8-h)h = 8h-h^2 =a

there are a couple of ways to finding the maximum area. You could plot area against h and find where h is a maximum.

Alternatively the area is a maximum when da/dh=0

da/dh=8-2h, which is zero when h=4

i.e. the maximum area is when h=4 and w=4

so the largest area is 16 m^2

To find the largest area of a rectangular area that can be enclosed by a given fence length, we need to apply some mathematical reasoning:

Let's assume the length of the rectangle is L and the width is W.

The perimeter of a rectangle is given by the formula:
Perimeter = 2L + 2W

In this case, we know that the perimeter is 16 meters. So we can write the equation as:
2L + 2W = 16

Simplifying the equation further, we get:
L + W = 8

To maximize the area, we can use the fact that the area of a rectangle is given by the formula:
Area = Length × Width

We can rewrite the formula to express the width in terms of the length:
W = 8 - L

Substituting this equation into the area formula, we have:
Area = L × (8 - L)

Now, we need to find the maximum value of the area. This can be done by finding the vertex of the quadratic equation Area = L × (8 - L).

To find the vertex, we can either complete the square or use the fact that the vertex occurs at the midpoint of the x-values of the equation. In this case, because we are dealing with a quadratic equation with a maximum point, the midpoint of the x-values is the maximum point.

The midpoint value of L can be found by using:
Midpoint of L = (minimum value of L + maximum value of L) / 2

Since the minimum value of L is 0 (a rectangle with only width) and the maximum value of L would be half of the perimeter (16/2 = 8), the midpoint value of L is:
Midpoint of L = (0 + 8) / 2 = 4

Now we can substitute this midpoint value back into the equation to find the maximum area:
Area = 4 × (8 - 4)
Area = 4 × 4
Area = 16 square meters

Therefore, the largest area of a rectangular area that can be enclosed by a 16-meter fence is 16 square meters.