Factoring Word problem

Question

You have a rectangular stained glass window that measures 3 feet by 2 feet. You have 6 square feet of glass with which to make a border of uniform width around the window. Find the area. Write a verbal model and then writ an equation that you can use to find the uniform width of the border. Solve your equation what should be the width of your border?

Answer 1

Kayla,

 

First of all we have window which measures 3' by 2', so it has an area (length x width) of 3' x 2' =  6 sq ft.

Now our border is also 6 square feet so our total for both window and border is 12 sq ft.

 

To find the width of our border we have to keep in mind that our border needs to cover not only the top and bottom and both sides, but also the 4 corners!

 

Let's call the width "x".  Then to cover the top and bottom we will need 2 strips of length 2' and width x, so the area of each strip will be 2x.

 

For the sides we need 2 strips of length 3' and width x, so the area of each side is 3x.

 

Each corner will be a square of area x² and we need 4 of those.

 

Adding it all together gives us:  

 

4x² + 2(3x) + 2 (2x) = 6 sq. ft

 

or

 

4x² + 10x - 6 = 0

 

Solving for the roots we get:

 

(2x + 6)(2x-1) = 0

 

So our roots are x = -3 and x = +½

 

having a "negative width" is meaningless, so our correct answer will be:

 

x = ½ ft.