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Question

Part 1
You look at a button under a magnifying glass. Find the actual length of the button.
The image of the button is 55 times the​ button's actual size and has a diameter of 99 cm.
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Part 1
The​ button's actual diameter is enter your response here cm.

Answer 1

To find the actual diameter of the button, you can use the magnification formula:

\[ \text{Magnification} = \frac{\text{Image size}}{\text{Actual size}} \]

In this case, the magnification is 55 times, and the image size (diameter of the image) is 99 cm. Let \( x \) be the actual diameter of the button. Thus, we have:

\[ 55 = \frac{99 \text{ cm}}{x} \]

To solve for \( x \), rearrange the equation:

\[ x = \frac{99 \text{ cm}}{55} \]

Now, perform the division:

\[ x = \frac{99}{55} \approx 1.8 \text{ cm} \]

So, the button's actual diameter is approximately 1.8 cm.