Advanced Algebra 2 for Precalc

Question

You are making a coffee table with a glass top surrounded by a cherry wood 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

Cherry wood of area to border and sorround glass of area 9 square feet. Thus the combined area will be area of glass + area of the border made from cherry wood

So total area of coffee table would be 9 + 7 = 16 square feet.

Since the center glass piece is a square thus the sorrouding border of cherry wood also would be of square shape. Thus the overall area of the square coffee table is 16 square feet.

So each side of the square is Sqrt(16) = 4 feet

Thus the outside of cherry border has 4 feet length and width while the insde of cherry border, which is same as the length and width of glass is 3 feet.

Thus the difference is 4 -3 =1 feet. Since border is on both sides therefore the width of the border= 1/2 feet i.e. 0.5 feet width.

Answer 2

Area of the inside = 9

Area of the outside = (3+2x)²

7=area of the border=9+12x+4x²

Solve the quadratic for x.

BTW: think about what wood you would likely actually have.

If you were lucky, you would actually have 7 board feet.