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Custom drapes are being fitted for a large circular window. The window has an 8 ft horizontal shelf with a 2 ft brace that sits in the frame. If the brace is extended upward, it would go through the center of the shelf and the circle. What is the diameter of the window?

Diameter [tex]$=$[/tex] [tex]$\square$[/tex] feet

Sagot :

GinnyAnswer
To determine the diameter of the window, we'll consider the information given and follow step-by-step reasoning:

1. The brace is mentioned to be 2 feet long. Since the brace goes through the frame and extends upward through the center, it functions as the radius of the circular window.

2. In a circle, the radius is half the length of the diameter.

3. Therefore, to find the diameter, we need to double the radius.

Since the radius is given as 2 feet, the diameter of the circular window is:

[tex]\[ \text{Diameter} = 2 \times \text{radius} = 2 \times 2 \text{ feet} = 4 \text{ feet} \][/tex]

So, the diameter of the window is:

[tex]\[ \boxed{4 \text{ feet}} \][/tex]
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