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

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

`(b)\ Scale\ width =(16)/(3)\ in`

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 = (Scale\ length)/(Actual\ length)`

`k_2 = (8in)/(24ft)`

Simplify

`k_2 = (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 = (Scale\ width)/(Actual\ width)`

`(1in)/(3ft) = (Scale\ width)/(16ft)`

The 16 is gotten from:

`Width = 8 * 2ft = 16ft`

So, we have:

`Scale\ width = 16ft * (1in)/(3ft)`

`Scale\ width = 16 * (1in)/(3)`

`Scale\ width =(16\ in)/(3)`

`Scale\ width =(16)/(3)\ in`

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