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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

14
14

3.5
3.5

12
12

2

1 answer

To determine the new length in boxes when converting the scale from 1 box = 6 meters to 1 box = 3 meters, we first need to calculate the actual length that corresponds to the original scale.

  1. The length of the rectangle in boxes is 7.
  2. At the original scale (1 box = 6 meters), the actual length is: \[ 7 \text{ boxes} \times 6 \text{ meters/box} = 42 \text{ meters} \]

Now, we need to convert this length into boxes using the new scale (1 box = 3 meters):

  1. To find out how many boxes correspond to 42 meters at the new scale, we perform the following calculation: \[ \frac{42 \text{ meters}}{3 \text{ meters/box}} = 14 \text{ boxes} \]

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