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