The regular pentagon below is a scale drawing of an original pentagon that was made by using a scale factor of One-fourth. A hexagon with side lengths of 5.5 inches. If each side of the pentagon has the same measure, which applies to the original pentagon? Select three options.

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

The missing options are:

Option A:The scale drawing represents a reduction.

Option B: Each side of the original is 22 inches long.

Option C: One side of the model can be 1.375 inches.

Option D: The scale drawing is proportional to the original.

Option E: The scale factor is multiplied by 5.5 to get the dimensions of the original.

So, we're given that:

Scaled pentagon's side length = length of sides of hexagon of 5.5 inches.
Scale factor = 1/4 = 0.25

Suppose the original size of the side length of the original pentagon was 'x' inches. (suppose scaling is from inch level to inch level as scale factor is given to be one-fourth and no unit is provided).

Then, we get:

Side length of scaled pentagon = scale factor × side length of orignal pentagon

or

[tex]5,5 = \dfrac{1}{4} \times x\\\\x = 5.5 \times 4= 22 \: \rm inches[/tex]

Thus, side length of the original pentagon was 22 inches.

Checking all the options one by one:

Option A: The scale drawing represents a reduction.

True.
Since the scaled pentagon had sides of 5.5 inches, and original one has 22 inches length of each side, that means the original pentagon was reduced to make the scaled pentagon (well if we get scale factor < 1, then that means the object is going to get smaller for sure).

Option B: Each side of the original is 22 inches long.

True, as obtained in the calculations done above.

Option C: One side of the model can be 1.375 inches.

False.

Option D: The scale drawing is proportional to the original.

True

Side length of scaled pentagon = scale factor × side length of orignal pentagon

That shows that the scale drawing is proportional to the original. as increasing side of either scaled pentagon or original pentagon will increase the other pentagon's sides.

Option E: The scale factor is multiplied by 5.5 to get the dimensions of the original.

False.

Side length of scaled pentagon = scale factor × side length of orignal pentagon

or

Side length of scaled pentagon = 4 × side length of orignal pentagon

That means:

Side length of orignal pentagon = (1/4) ×Side length of scaled pentagon

Since 1/4 = 0.25 and not 5.5 , so this option is false.

Thus, the statement that applies to the original pentagon are:

Option A: The scale drawing represents a reduction.
Option B: Each side of the original is 22 inches long.
Option D: The scale drawing is proportional to the original.

Learn more about scale factors here :

https://brainly.com/question/8765466