Answer:
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.