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1. A figure is dilated by a factor of 6 . By what factor will the perimeter of the figure change? 1 6 12 36

Ask by Flynn Floyd. in the United States
Feb 03,2025

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Answer

The perimeter will change by a factor of 6.

Solution

When a figure is dilated by a certain factor, all linear dimensions (such as lengths, perimeters, and heights) are multiplied by that factor. In this case: - The dilation factor is **6**. - The **perimeter** of the figure, which is a linear measure, will also be multiplied by **6**. **Therefore, the perimeter will change by a factor of 6.** **Answer:** 6

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Beyond the Answer

When a figure is dilated by a factor of 6, each linear dimension of the figure, including its perimeter, also changes by that same factor. Therefore, if the original perimeter is P, the new perimeter after dilation will be 6P. This means the perimeter will change by a factor of 6. But the options given are a bit of a puzzle, right? To further clarify, if you think of it in terms of area, that would change by a factor of \(6^2 = 36\), which is probably where the 36 option comes from. Keep that in mind while working with similar figures! To apply this in the real world, consider how scale models operate. If you scale up a model vehicle for a display, the distance around that vehicle—its perimeter—grows in the same ratio as the model itself. Dilation helps architects and designers visualize projects at different scales, ensuring everything fits perfectly when built!

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