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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.

User Pmarflee
by
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1 Answer

5 votes

Answer:

  • 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.

User Harryt
by
8.2k points

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