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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?

User Coo
by
6.4k points

2 Answers

4 votes

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

Step-by-step explanation:

User Ricky
by
6.9k points
3 votes

Answer:


(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

User Sebastian Busek
by
7.2k points
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