Respuesta :
Answer:
Length = 12.5 feet
Width = 12.5 feet
Step-by-step explanation:
We can set two equations to solve this problem.
First equation:
The perimeter of a rectangle is 2*L + 2*W, where L is the lenght and W is the width, and Noah has 50 feet of fencing to use, so:
2*L + 2*W = 50
Second equation:
The area of the rectangle (A) is calculated mutiplying the lenght by the width:
A = L * W
Dividing the first equation by 2 and isolating L, we have:
L + W = 25 -> L = 25 - W
Using this equation in the second one, we have:
A = (25 - W)*W = 25W - W^2
The formula to calculate the point that gives the maximum value is:
x = –b/2a
So, the value of W that gives the maximum area will be:
W = -25/2*(-1) = -25/(-2) = 12.5 feet
Using this value in the first equation W + L = 25, we have:
12.5 + L = 25
L = 12.5 feet
So, the length and width that produce the largest possible area are 12.5 feet and 12.5 feet.
