Question

Above are two different models of the same rectangle. If the width of the model on the left is 11 in, what is the width of the model on the right? A. 3.67 in B. 4 in C. 12.25 in D. 19.25 in

Answer 1

By using the scale factors provided, the width of the model on the right is calculated to be 4 inches, which is option B.

Step-by-step explanation:

The question asks for the width of a rectangle model when converted from one scale to another. Given that the width of the model on the left is 11 inches and the scale factor is 1 inch = 3 feet for the first rectangle, we can calculate the actual width in feet. Then, using the scale factor for the second rectangle where 1 inch = 8.25 feet, we can determine the width in inches for the model on the right.

Step 1: Convert the width of the first model to actual size.

11 inches * 3 feet/inch = 33 feet (actual width)

Step 2: Convert the actual width to the width of the second model using its scale factor.

33 feet / 8.25 feet/inch = 4 inches

The width of the model on the right is therefore 4 inches, which corresponds to option B.

Answer 2

Given the information about the two rectangles, we know that the width of the left model is 1 inch for 3 feet. That means the actual width would be;

`\begin{gathered} W=1*3ft \\ W=11*3ft \\ W=33ft \end{gathered}`

Similarly, for the model on the right;

`\begin{gathered} W=1*8.25ft \\ W=11*8.25ft \\ W=90.75ft \end{gathered}`

Next we are told that the width of the left rectangle is 11 inches. Note that what we have is two rectangles that are both models of the same rectangle. Which means, there is a common ratio for any dimensions given. If now the width of the left rectangle is given as 11 inches, we can set up an equation like this;

`(33*12in)/(11)=(90.75*12in)/(x)`

Note here that we are converting 33 feet and 90.75 feet into inches when we multiply by 12 (1 foot = 12 inches).

`\begin{gathered} (33*12)/(11)=(1089)/(x) \\ 36=(1089)/(x) \\ We\text{ now cross multiply and we have;} \\ x=(1089)/(36) \\ x=30.25 \end{gathered}`

ANSWER:

The width of the model on the right would be 30.25 inches