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Daniel [21]
3 years ago
8

15 POINTS A 4-inch length is represented as 1/8 on a scale drawing. What is the scale used on the drawing?

Mathematics
1 answer:
-BARSIC- [3]3 years ago
8 0

9514 1404 393

Answer:

  (b)  1 foot = 3/8 inch

Step-by-step explanation:

The given ratio is ...

  actual : scale = 4" : 1/8"

You know that 1 foot = 12 in = 3×4 in, so you can multiply the above ratio by 3 to see what it is for 1 foot.

  actual : scale = 3×4" : 3×1/8"

  = 12" : 3/8"

  = 1 foot : 3/8 in

______

<em>Alternate approach</em>

Essentially, we're saying that the ratios between actual measures and those on a scaled drawing or model form a proportion.

  scale / actual = (1/8")/(4 in) = ??/(12 in)

Multiplying by 12 in, we get ...

  ?? = (12 in)(1/8")/(4 in) = 3×1/8"

  ?? = 3/8"

__

<em>More detail</em>

Notice that this only works when the units in the ratio (12 in)/(4 in) cancel to give a pure number 12/4 = 3.

If we had put 1 foot in the proportion, then we would end up with ?? being expressed in feet, not inches:

  (1/8")/(4") = ??/(1 ft)

  ?? = (1 ft)(1/8")/(4") = (1 ft)(1/32) = 1/32 ft

Then, to find the answer to the question, we would have to find out how many inches is 1/32 ft.

  1/32 ft = (1/32)(12 in) = 12/32 in = 3/8 in

__

<em>End comment</em>

For best results, the units in corresponding parts of a proportion should be the same.

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