# Baileys rectangular dog pen for his Irish setter must have an area of 400 square feet. Also, the length must be 10 feet longer than the width. How do you find the dimensions of the pen?

May 11, 2016

Width = 15.616 feet, length is 25.616 feet.

#### Explanation:

Start with a sketch of a rectangle. Let $x$ be the width.

The length is 10 feet longer, so the length is $\left(x + 10\right)$

The area is found from $l \times w$, but this must be 400.

Make an equation in $x$ and solve it. Once you know the value of $x$ you can find y

$\Rightarrow \text{ } x \left(x + 10\right) = 400$

${x}^{2} + 10 x - 400 = 0 \text{ " "factors are not obvious}$

Completing the square method probably easiest.

${x}^{2} + 10 x + 25 = 400 + 25$
${\left(x + 5\right)}^{2} = 425$
x + 5 = +-sqrt425)#
$x = \sqrt{425} - 5 \text{ } \mathmr{and} x = - \sqrt{425} - 5$

$x = 15.616 \text{ } \mathmr{and} x = - 25.6163$