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

Answer:

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

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

Step-by-step 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

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

32-2x = 32 - 2•8 = 16