Question

Solve by using methods of factoring, the square root principle, or the quadratic formula. Round your answers to the nearest tenth.

A rectangular table for the dining room has a surface area of 18 square feet. The length is five more feet than twice the width of the table. Find the length and width (in ft) of the table.

Answer 1

• length: 9 ft
• width: 2 ft

Explanation:

You want the length and width of an 18 square foot table that is 5 feet longer than twice the width.

Setup

Let w represent the width of the table. Then the length is (5+2w) and the area is (length×width) = (5+2w)(w). The area is 18 square feet, so we have ...

(5 +2w)(w) = 18

Solution

Putting this in standard form, we get ...

2w² +5w -18 = 0

Factoring gives ...

(2w +9)(2w -4)/2 = 0

(2w +9)(w -2) = 0

w = -9/2 or 2 . . . . . . . . values that make the factors zero

The width cannot be negative, so must be 2 feet.

The length is ...

5 +2(2) = 9 . . . . feet

The table is 9 feet long and 2 feet wide.