Answer:
[tex](a)\ k_2 = 1in:3ft[/tex]
[tex](b)\ Scale\ width =\frac{16}{3}\ in[/tex]
Step-by-step explanation:
Given
[tex]k_1 = 1in : 2ft[/tex] --- Initial scale factor
[tex]Blueprint: 12in\ by\ 8in[/tex] --- Missing from the question
Solving (a): The new scale factor.
Convert the initial blueprint to actual measurement using the initial scale factor, we have:
[tex]Length = 12 * 2ft = 24ft[/tex]
[tex]Width = 8 * 2ft = 16ft[/tex]
From the question, we understand the new scale factor represents the width as 8in.
The scale factor (k2) is then calculated as:
[tex]k_2 = \frac{Scale\ length}{Actual\ length}[/tex]
[tex]k_2 = \frac{8in}{24ft}[/tex]
Simplify
[tex]k_2 = \frac{1in}{3ft}[/tex]
Represent as fraction
[tex]k_2 = 1in:3ft[/tex]
The above is the new scale factor
Solving (b): The new width
Using the scale factor above we have:
[tex]k_2 = \frac{Scale\ width}{Actual\ width}[/tex]
[tex]\frac{1in}{3ft} = \frac{Scale\ width}{16ft}[/tex]
The 16 is gotten from:
[tex]Width = 8 * 2ft = 16ft[/tex]
So, we have:
[tex]Scale\ width = 16ft * \frac{1in}{3ft}[/tex]
[tex]Scale\ width = 16 * \frac{1in}{3}[/tex]
[tex]Scale\ width =\frac{16\ in}{3}[/tex]
[tex]Scale\ width =\frac{16}{3}\ in[/tex]
Hence, the scale width of the blueprint is: 16/3 inches
