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Item 22 You are making a blueprint of your house. You measure the lengths of the walls of your room to be 11 feet by 12 feet. When you draw your room on the blueprint, the lengths of the walls are 8.25 inches by 9 inches. What scale factor dilates your room to the blueprint?

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Answer:

[tex]\frac{1}{16}[/tex]

Explanation:

Converting feet to inches

[tex]1\ ft=12\ inches[/tex]

[tex]11\ ft=11\times 12\inches\\ =132\ inches[/tex]

[tex]12\ ft=12\times 12\\ =144\ inches[/tex]

Blueprint length 8.25 inches and 9 inches

Dividing the lenghts of the blueprint by the room

[tex]\frac{8.25}{132}=\frac{1}{16}[/tex]

[tex]\frac{9}{144}=\frac{1}{16}[/tex]

Hence, the scale factor that dilates your room to the blueprint is

[tex]\frac{1}{16}[/tex]

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