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During the day, Lola's dog is tied by rope to a tree in the center of her yard. The scale drawing below shows the area that the dog has to run. If the actual length of the rope is 12 1/2 feet, what is the scale used in the drawing? 1 9/16

Sagot :

MrRoyal

Answer:

[tex]Actual\ Length : Scale\ Length = 8 : 1[/tex]

Step-by-step explanation:

Given

[tex]Actual\ Length = 12\frac{1}{2}ft[/tex]

[tex]Scale\ Length = 1\frac{9}{16}ft[/tex] --- See attachment

Required

Determine the scale used

The scale of the drawing can be represented using the following ratio

[tex]Scale = Actual\ Length : Scale\ Length[/tex]

Substitute values for actual and scale lengths

[tex]Scale = 12\frac{1}{2}: 1\frac{9}{16}[/tex]

Convert to improper numbers

[tex]Scale = \frac{25}{2}: \frac{25}{16}[/tex]

Convert to division:

[tex]Scale = \frac{25}{2}/\frac{25}{16}[/tex]

[tex]Scale = \frac{25}{2}*\frac{16}{25}[/tex]

[tex]Scale = \frac{1}{2}*\frac{16}{1}[/tex]

[tex]Scale = \frac{16}{2}[/tex]

[tex]Scale = \frac{8}{1}[/tex]

Convert to ratio

[tex]Scale = 8 : 1[/tex]

Hence, the scale of the drawing is:

[tex]Actual\ Length : Scale\ Length = 8 : 1[/tex]

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