Welcome to the article A rectangular stained glass window is 2 feet by 4 feet A clear glass border is constructed around the stained glass window The border is. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
The width of the border around the stained glass window is approximately 1.15 feet, calculated by subtracting the stained glass area from the total area including the border.
To find the width of the border, we need to subtract the area of the stained glass window from the total area including the border.
Given:
- Length of stained glass window = 4 feet
- Width of stained glass window = 2 feet
- Area of stained glass window = [tex]\(4 \times 2 = 8\)[/tex] square feet
- Total area including the border = Area of stained glass window + Area of border = 8 + 7 = 15 square feet
Let's denote the width of the border as x feet.
The total length including the border is 4 + 2x feet, and the total width including the border is 2 + 2x feet.
The area of the total window with the border is the product of its length and width:
(4 + 2x)(2 + 2x) = 15
Expanding this equation:
8 + 4x + 4x + 4x^2 = 15
8 + 8x + 4x^2 = 15
4x^2 + 8x - 7 = 0
Now, let's solve this quadratic equation using the quadratic formula:
[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]
Where a = 4, b = 8, and c = -7.
[tex]\[x = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 4 \times (-7)}}}}{{2 \times 4}}\][/tex]
[tex]\[x = \frac{{-8 \pm \sqrt{{64 + 112}}}}{8}\][/tex]
[tex]\[x = \frac{{-8 \pm \sqrt{{176}}}}{8}\][/tex]
[tex]\[x = \frac{{-8 \pm 4\sqrt{{11}}}}{8}\][/tex]
[tex]\[x = \frac{{-2 \pm \sqrt{{11}}}}{2}\][/tex]
Since the width cannot be negative, we take the positive root:
[tex]\[x = \frac{{-2 + \sqrt{{11}}}}{2} \approx 1.15 \text{ feet}\][/tex]
Therefore, the width of the border is approximately 1.15 feet.
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Rewritten by : Brahmana