# You have 188 feet of fencing to enclose a rectangular region. What is the maximum area?

Apr 9, 2016

$2209$ square feet

#### Explanation:

$1$. Make "let" statements to represent the length and width of the rectangular region.

Let $x$ represent the length.
Let $\frac{188 - 2 x}{2} = 94 - x$ represent the width.

$2$. Create an algebraic expression represent the area of a rectangle.

${A}_{\text{rectangle}} = x \left(94 - x\right)$

$3$. Complete the square.

${A}_{\text{rectangle}} = 94 x - {x}^{2}$

${A}_{\text{rectangle}} = - \left({x}^{2} - 94 x\right)$

${A}_{\text{rectangle}} = - \left({x}^{2} - 94 x + {\left(- \frac{94}{2}\right)}^{2} - {\left(- \frac{94}{2}\right)}^{2}\right)$

${A}_{\text{rectangle}} = - {\left(x - 47\right)}^{2} + 2209$

$\therefore$, the maximum area of the rectangular region is $2209$ square feet.