Use the image to answer the question.

Question

A grid is shown with a rectangle drawn on it. The rectangle is 10 units long and 2 units wide, labeled with 10 and 2 respectively.

Scale factor: 1 box = 6 inches

Maisie needs to convert this scale drawing from a scale factor of 1 box = 6 inches to a scale factor of 1 box = 12 inches. The length in the scale drawing shown is 10 boxes. What will be the length of the boxes in the new drawing?

(1 point)
Responses

12
12

5
5

1
1

20

Answer 1

To convert the length of the rectangle from the current scale of 1 box = 6 inches to the new scale of 1 box = 12 inches, we need to determine what the length will be in the new scale.

Currently, the length of the rectangle is 10 boxes. Since 1 box = 6 inches, we can calculate the current length in inches:

Current length in inches: $10\text{ boxes}\times 6\text{ inches/box}=60\text{ inches}$

Now, we need to convert this length into the new scale where 1 box = 12 inches. To find out how many boxes this length corresponds to in the new scale, we divide the total length in inches by the value of 1 box in the new scale:

New length in boxes: $\frac{60\text{ inches}}{12\text{ inches/box}}=5\text{ boxes}$

So, the length of the boxes in the new drawing will be 5. Therefore, the correct response is:

5