# The length of a rectangular deck is 5 feet longer than its width, x. The area of the deck is 310 square feet. What equation can be used to determine the width of the deck?

Jul 9, 2017

see explanation

#### Explanation:

The area of a quadrilateral (which includes rectangles) is $l \times w$ or length times width. The area here is stated to be 310 square feet ($f {t}^{2}$).

We're told that the length is 5 feet longer than the width, and that $x$ represents the width. Thus...

$l = 5 + x$
$w = x$
$\setminus \therefore l \times w = \left(5 + x\right) \setminus \cdot \left(x\right) = 310$ $f {t}^{2}$

Now you have an algebraic variable question to solve.

• $\left(5 + x\right) \setminus \cdot \left(x\right) = 310$
• Apply Distributive Property: $x \left(5\right) + x \left(x\right) = 310$
• $5 x + {x}^{2} = 310$, moving everything to one side gets you a quadratic:
• ${x}^{2} + 5 x - 310 = 0$