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Welcome to the article A rectangular stained glass window measures 2 feet by 4 feet A clear glass border is constructed around the stained glass window The width of. 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!

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

Answer :

The width of the clear glass border is approximately 0.73 feet.

To find the width of the clear glass border around the stained glass window, you can set up an equation based on the given information.

Let's denote the width of the border as "x" feet.

The overall dimensions of the window and the border are as follows:

Length: 2 feet (stained glass) + 2x (border) + 2x (border) = 2 + 4x

Width: 4 feet (stained glass) + 2x (border) + 2x (border) = 4 + 4x

The area of the clear glass border is given as 7 square feet.

So, we can set up the equation for the area of the border:

Area of border = (Length of border + Width of border) * 2 * x = 7

Plug in the values:

(2 + 4x + 4 + 4x) * 2x = 7

Simplify the equation:

(6x + 6) * 2x = 7

Now, distribute the 2x on the left side:

12x^2 + 12x = 7

Subtract 7 from both sides to set the equation equal to 0:

12x^2 + 12x - 7 = 0

Now, you can solve this quadratic equation for "x." You can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 12, b = 12, and c = -7. Plug in these values:

x = (-12 ± √(12^2 - 4 * 12 * (-7))) / (2 * 12)

x = (-12 ± √(144 + 336)) / 24

x = (-12 ± √480) / 24

x = (-12 ± 4√30) / 24

Now, simplify further:

x = (-1/2) ± (√30 / 6)

The two possible solutions for "x" are:

x = (-1/2) + (√30 / 6)

x = (-1/2) - (√30 / 6)

The first solution is a positive value, so that's the width of the border:

x = (-1/2) + (√30 / 6) ≈ 0.73 feet

So, the width of the clear glass border is approximately 0.73 feet.

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Rewritten by : Brahmana