Lindsey has 45ft of metal fencing to form 3 sides of a rectangular garden. A tall wooden fence already in place will serve as the fourth side. What lengths of fencing will produce the largest area?

To answer this item, we let L be the length and W be the width. The area of the rectangles is calculated through the equation,

Area = L x W

From the given scenario, we can deduced that,

L + 2W = 48

Such that L = 48 - 2W.

Substituting this to the equation for area,

Area = (48 - 2W) (W)

Simplifying,

Area = 48W - 2W²

Differentiating and equating to zero,

dArea = 48 - 4W = 0

The value of W from the equation is 12. Hence,

L = 48 - 2W = 48 - 2 (12) = 24

The dimensions are:

Length = 24 ft

Width = 12 ft