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

2
2

14
14

3.5

Answer 1

To convert the scale drawing from a scale factor of 1 box = 6 meters to a scale factor of 1 box = 3 meters, we need to understand how the length in boxes will change with the new scale.

1. Current scale length in meters:

   • The rectangle's length is 7 boxes, and with the current scale (1 box = 6 meters), the length in meters is: \[ 7 \text{ boxes} \times 6 \text{ meters/box} = 42 \text{ meters} \]

2. New scale length in boxes:

   • With the new scale (1 box = 3 meters), we need to convert the 42 meters back to boxes by dividing by 3 meters/box: \[ \frac{42 \text{ meters}}{3 \text{ meters/box}} = 14 \text{ boxes} \]

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

The correct response is 14.