Question

You just discovered that you have 100 feet of fencing and you have decided to make a rectangular garden. What is the largest area you can enclose using the materials you have? You must set up an equation and solve.

Answer 1

The area is:
 A = x * y
 The perimeter is:
 P = 2x + 2y = 100
 We clear y:
 2y = 100-2x
 y = 50-x
 We write the area in terms of x:
 A (x) = x * (50-x)
 Rewriting:
 A (x) = 50x-x ^ 2
 Deriving:
 A '(x) = 50-2x
 We equal zero and clear x:
 50-2x = 0
 x = 50/2
 x = 25
 Then, the other dimension is given by:
 y = 50-x
 y = 50-25
 y = 25
 Therefore, the largest area is:
 A = (25) * (25)
 A = 625 feet ^ 2
 Answer:
 the largest area you can enclose using the materials you have is:
 A = 625 feet ^ 2