Use the image to answer the question.

Question

A grid is shown with a rectangle drawn on it. The rectangle is 7 units long and 1 unit wide, labeled with 7 and 1 respectively.

Scale factor: 1 box = 6 meters

L’Quan needs to convert this scale drawing from a scale factor of 1 box = 6 meters to a scale factorof 1 box = 3 meters. The length in the scale drawing shown is 7 boxes. What will be the length in boxes of the new drawing?.

(1 point)
Responses

12
12

3.5
3.5

14
14

2
2

Answer 1

To convert the length from a scale of 1 box = 6 meters to a scale of 1 box = 3 meters, we need to consider how the scaling affects the dimensions.

In the original scale, the rectangle is 7 boxes long. Since 1 box represents 6 meters, the length in meters is calculated as follows:

\[ \text{Length in meters} = 7 , \text{boxes} \times 6 , \text{meters/box} = 42 , \text{meters} \]

Now, to find the equivalent length in boxes when using the new scale of 1 box = 3 meters, we divide the total length in meters by the new scale:

\[ \text{Length in boxes} = \frac{42 , \text{meters}}{3 , \text{meters/box}} = 14 , \text{boxes} \]

Therefore, the length in boxes of the new drawing will be 14.

The correct response is 14.