Answer:
Step-by-step explanation:
Total fencing David has = 480 yards
Means He can surround all 4 sides of the rectangular area using this fencing.
We can say that the total fencing he has in terms of length L and width W of the rectangle will be L+L+W+W = 480
So , 2(L+W) =480
Divide both sides by 2 to get
L+W = 240
Subtract W from both sides so we get L in terms of W
L= 240 - W
(a) We know that the area of a rectangle is Length times width (L × W)
So , Area = (240-W) W
Area = 240W - W^2
(b) By comparing the area equation with ax^2+bx+c (standard quadratic equation)
we get a=-1 and b =240
Area is maximum when
[tex]W = \frac{-b}{2a} \\W= \frac{-240}{2(-1)} \\W = 120[/tex]
So for W = 120 yd the area is largest .
(c) Maximum area of the rectangle can be found by plugging this W = 120 in the Area equation that we got in part (a)
So the maximum area ,
A = [tex]240 (120) - 120 ^2[/tex]
A =28800-14400
A = 14400
Hence Maximum area = 14400 sq yd
