Question

Suppose you still have 200 feet of fencing to enclose a rectangular garden. But this time to

Answer 1

Answer:

a. Area = (200 - 2*Width) * Width

b. Length = 100 feet and Width = 50 feet

c. Area = 5000 ft2

d. 2500 ft2 more area

Step-by-step explanation:

The perimeter of a rectangle is given by: P = 2L + 2W, where L is the length and W is the width. The area of the rectangle is given by A = L * W.

As we will use one side of the rectangle as a wall, the perimeter of fence used will be:

P = L + 2W = 200

From this equation, we have L = 200 - 2W

Using this value of L in the area equation, we have:

A = (200 - 2W) * W = 200W - 2W^2

To find the maximum value of A, we need to find the vertix of the quadratic equation, and to do so we can use the following formula:

x_v = -b/2a = -200 / (-4) = 50

Using W = x_v = 50, we have that:

L = 200 - 2*50 = 100

A = L * W = 5000 ft2

If we didn't use the wall, the maximum area would be given by a square format, with length = 50 feet and width = 50 feet, giving the area of 50*50 = 2500 ft2

So the increase in the area was 5000 - 2500 = 2500 ft2