What should the width of the border be?

Question

you have a rectangupar stained glass window that measures 2 feet by 1 foot. You have 4 square feet of glass with which to make a border of uniform width around the window.

Answer 1

Hi Megan,

 

Let x = the width of the uniform border

 

and we know that we want to add 4 ft to the area

 

so our new window will have area of 4 + 2 (from the original)  = 6

 

and our new length will be L + 2x

 

our new width will be w + 2x

 

but we know L = 2 and w = 1

 

so

 

(L + 2x) = 2 + 2x

 

(w + 2x) = 1 + 2x

 

 

and now Area = 6 = (2+2x)(1+2x)

 

6 = 2 + 6x + 4x²

 

4x² +6x -4 = 0

 

(4x-2)(x+2)=0

 

we can only use one of these factors becasue the other gives us a negative value for x

 

4x - 2 = 0

 

x = .5

 

so our border will be a uniform width of .5 ft

 

and checking it (L + 1)(w+1) = 3 *2 = 6 sq ft

 

Hope this helps

Answer 2

Hi Megan,

             What you need to do is translate the information given into an equation that relates the unknown width,w to the known size of the window and available area of glass for the border.

 

first we will calculate the areas going around the window: 2w+w+2w+w=4, addend the w's together gives 6w=4 so w=4/6ft or 3/4ft or 9 inches. So with 4 square feet of glass we can make a 9" border around the window.

 

Regards

Jim