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?

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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?

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Answer 1 · 2017-07-09T23:51:16

see explanation

Explanation:

The area of a quadrilateral (which includes rectangles) is $lxxw$ or length times width. The area here is stated to be 310 square feet ( $ft^2$ ).

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

$l=5+x$
$w=x$
$\thereforelxxw=(5+x)\cdot(x)=310$ $ft^2$

Now you have an algebraic variable question to solve.

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

Solving by Quadratic Formula

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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?

1 Answer

Explanation:

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