Question

You are making a coffee

table with a glass top surrounded by a cherry border.
The glass is 3 feet by 3 feet. You want the cherry border
to be a uniform width. You have 7 square feet of cherry
to make the border. What should the width of the border be?

Answer 1

6 inches

Explanation:

You want to know the uniform width of border around a 3 ft square coffee table that would have an area of 7 square feet.

Border area

The area of the border is x feet wide by 3 feet long along each of the 4 sides, together with 4 corner squares that are x ft square.

A = 7 = 4(3x +x²)

Completing the square, we have ...

x² +3x +9/4 = 7/4 +9/4 . . . . . . divide by 4, add (3/2)² to both sides

(x +3/2)² = 4 . . . . . . . . . . . . simplify

x +3/2 = √4 = 2 . . . . . . square root

x = 1/2 . . . . . . . . . foot

The width of the border should be 6 inches.