Question

An architect is recreating the blueprint for a deck with an existing scale factor of 1 in. equals 2 ft​, that is shown. The architect is using a different scale so that the length of the same deck on the new blueprint measures 8 inches. Complete parts a and b. What is the scale factor of the new blue print? 1 inch = ______feet.
Part 2: What is the width of the deck on the new​ blueprint?

Answer 1

Answer: Part A is 3 and part b is 5 1/3 inches

Step-by-step explanation:

Answer 2

Answer:

$(a)\ k_2 = 1in:3ft$

$(b)\ Scale\ width =\frac{16}{3}\ in$

Step-by-step explanation:

Given

$k_1 = 1in : 2ft$ --- Initial scale factor

$Blueprint: 12in\ by\ 8in$ --- Missing from the question

Solving (a): The new scale factor.

Convert the initial blueprint to actual measurement using the initial scale factor, we have:

$Length = 12 * 2ft = 24ft$

$Width = 8 * 2ft = 16ft$

From the question, we understand the new scale factor represents the width as 8in.

The scale factor (k2) is then calculated as:

$k_2 = \frac{Scale\ length}{Actual\ length}$

$k_2 = \frac{8in}{24ft}$

Simplify

$k_2 = \frac{1in}{3ft}$

Represent as fraction

$k_2 = 1in:3ft$

The above is the new scale factor

 Solving (b): The new width

Using the scale factor above we have:

$k_2 = \frac{Scale\ width}{Actual\ width}$

$\frac{1in}{3ft} = \frac{Scale\ width}{16ft}$

The 16 is gotten from:

$Width = 8 * 2ft = 16ft$

So, we have:

$Scale\ width = 16ft * \frac{1in}{3ft}$

$Scale\ width = 16 * \frac{1in}{3}$

$Scale\ width =\frac{16\ in}{3}$

$Scale\ width =\frac{16}{3}\ in$

Hence, the scale width of the blueprint is: 16/3 inches