Question

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?

Answer 1

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`

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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