Question

A beetle that Hannah observed was too small to draw at its actual size. Hannah decided to make a scale drawing of the beetle as shown above. The beetle in the drawing is 7.62 cm long and 3.81 cm wide. The scale factor of her drawing is 3. Part A: Find the actual length of the beetle Hannah observed. Show all work. Part B: Find the actual width of the beetle Hannah observed. Show all work. Part C: The actual length of each of the beetle's antennae is 0.2 cm. What is the size of each antenna on Hannah's scale drawing? Show all work.

Answer 1

`Actual\ Length = 2.54\ cm`

`Actual\ Width = 1.27\ cm`

`Scale\ Length = 0.6\ cm` --- Beetle's antennae

Explanation:

Given

The following scale measurements

`Length = 7.62cm`

`Width = 3.81cm`

`Scale\ Factor = 3`

Solving (a): The actual length.

We simply divide the scale length by the scale factor.

`Actual\ Length = (Scale\ Length)/(Scale\ Factor)`

`Actual\ Length = (7.62cm)/(3)`

`Actual\ Length = 2.54\ cm`

Solving (b): The actual width.

We simply divide the scale width by the scale factor.

`Actual\ Width = (Scale\ Width)/(Scale\ Factor)`

`Actual\ Width = (3.81\ cm)/(3)`

`Actual\ Width = 1.27\ cm`

Solving (c):

Given: Actual Length of the beetle's antennae is 0.2 cm.

Required: Determine the scale measurement.

This is solved using:

`Actual\ Length = (Scale\ Length)/(Scale\ Factor)`

`0.2\ cm = (Scale\ Length)/(3)`

`Scale\ Length = 0.2cm * 3`

`Scale\ Length = 0.6\ cm`