Question

Julie will build a rectangular pen for her dog against a barn. A wall from the barn will form one side of the pen. She has 32 m of fencing to form the other three sides. She plans to build the pen so that it has its maximum possible area.

What will be the dimensions of Julie's pen?

Answer 1

The width (side perpedicular to the barn): x = 8 m

The lenght (side parallel to the barn): y = 16 m

Explanation:

x - the width of the barn

She has 32 m of fencing so for the lenght remain (32-2x) m of fencing:

y = 32 - 2x

Area of the fencing: A = x•y

A(x) = x•(32 - 2x)

A(x) = -2x² + 32x ← quadratic function

The maximum value of quadratic function occurs at:
`x=-\frac b{2a}`

a = -2, b = 32

`x=-\frac b{2a}=-(32)/(2\cdot(-2))=-(-8)=8`

32-2x = 32 - 2•8 = 16