A rectangular stained glass window is 2 feet by 4 feet. A clear glass border is constructed around the stained glass window. The width of the border is equal and was made out of 7 square feet of clear glass. What is the width of the border?

Answer 1

To find the width of the border, we first need to calculate the total area of the entire window including the border.

Area of the stained glass window = 2 ft x 4 ft = 8 square feet

Let x be the width of the border

Total area of the window with the border = (2+2x)(4+2x)

Total area = (2+2x)(4+2x) = 8 + 16x + 4x + 8x^2

Total area = 8 + 20x + 8x^2

Now we know that the border is made out of 7 square feet of clear glass, so:

Total area - Area of stained glass window = Area of clear glass border

8 + 20x + 8x^2 - 8 = 7

20x + 8x^2 = 7

8x^2 + 20x - 7 = 0

Solving for x using the quadratic formula:

x = (-b ± √(b^2-4ac)) / 2a
x = (-20 ± √(20^2-4*8*(-7))) / 2*8
x = (-20 ± √(400+224)) / 16
x = (-20 ± √624) / 16
x = (-20 ± 24.98) / 16

x ≈ (-20 + 24.98) / 16 ≈ 0.31 feet
x ≈ (-20 - 24.98) / 16 ≈ -2.80 feet

Since width cannot be negative, the width of the border is approximately 0.31 feet.