Question

You are making a 3 foot by 3 foot coffee table with a glass top surrounded by a cherry border of uniform width. The cherry border is included in the 3 x 3 measurements. You have 5 square feet of cherry border. What should the width of the border be?

Answer 1

Explanation:

The total area of the coffee table (including the cherry border) is:

3 feet x 3 feet = 9 square feet

We know that the area of the cherry border is:

5 square feet

To find the width of the cherry border, we need to subtract the area of the glass top from the total area of the coffee table:

9 square feet - area of glass top = area of cherry border

The area of the glass top is:

(3 feet - 2x) x (3 feet - 2x)

where x is the width of the cherry border.

Since the glass top is square, we can set the two dimensions equal to each other:

(3 feet - 2x) = (3 feet - 2x)

Expanding the left-hand side, we get:

9 feet - 6x = 9 feet - 6x

Simplifying, we get:

0 = 0

This means that the width of the cherry border does not affect the area of the glass top. Therefore, we can set the area of the glass top equal to the total area of the coffee table minus the area of the cherry border:

(3 feet - 2x) x (3 feet - 2x) = 9 square feet - 5 square feet

Simplifying, we get:

(3 feet - 2x) x (3 feet - 2x) = 4 square feet

Expanding the left-hand side, we get:

9 feet^2 - 12 feet x + 4x^2 = 4 square feet

Subtracting 4 square feet from both sides, we get:

9 feet^2 - 12 feet x + 4x^2 - 4 square feet = 0

Simplifying, we get:

4x^2 - 12 feet x + 9 feet^2 - 4 square feet = 0

Using the quadratic formula, we get:

x = [12 feet ± sqrt((12 feet)^2 - 4(4)(9 feet^2 - 4 square feet))] / (2(4))

Simplifying, we get:

x = [12 feet ± sqrt(144 feet^2 - 4(4)(9 feet^2 - 4 square feet))] / 8

x = [12 feet ± sqrt(144 feet^2 - 144 feet^2 + 64 square feet)] / 8

x = [12 feet ±