The maximum area that David can have is 10,000 yd^2
The formula for calculating the area of a rectangle is expressed as:
A = lw
If David has 400 yards of fencing, then;
P = 2(l +w)
400 = 2( l+ w)
200 = l + w
l = 200 - w
Substitute into the area
A = (200-w)w
A = 200w - w^2
If the area is maximized, then;
dA/dw = 0
dA/dw = 200 - 2w
2w =200
w = 100 yards
Recall that;
200 = l + w
l = 200 - 100
l = 100
The maximum area = 100 * 100
The maximum area = 10,000 yd^2
The maximum area that David can have is 10,000 yd^2
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