Bob has 60 feet of fencing, which he intends to use to enclose a rectangular garden. If the length of the garden is x feet long, he wants the width to be (40-2x) feet wide. What value of x will result in the largest area for the garden?

x = 10 feet.

Perimeter of a rectangle = 2 (l + w)

Area of a rectangle = w*l

P = 60ft

Length = x

Width = 40-2x

A = ?

60 = 2 (x + (40-2x)

60 = 2x + 80 - 4x

60 = - 2x + 80

2x = 80 - 60

2x = 20

2x / 2 = 20 / 2

x = 10 - - length

Width = 40 - 2x; where x = 10; 40 - 2 (10) = 40 - 20 = 20.

P = 2 (l + w)

60 = 2 (10 + 20)

60 = 2 (30)

60 = 60

Area = w * l

A = 20 * 10

A = 200 square feet