To determine which drawing correctly reproduces the playground with a new scale of 1 box = 20 meters, we need to consider how to convert the dimensions from the original scale (1 box = 5 meters) to the new scale.
If the original playground had dimensions of 2 boxes long and 1 box wide, for example:
- Length = 2 boxes × 5 meters/box = 10 meters
- Width = 1 box × 5 meters/box = 5 meters
To convert these dimensions to the new scale (1 box = 20 meters):
- Length = 10 meters ÷ 20 meters/box = 0.5 boxes
- Width = 5 meters ÷ 20 meters/box = 0.25 boxes
For the second example with dimensions of 3 boxes long and 2 boxes wide:
- Length = 3 boxes × 5 meters/box = 15 meters
- Width = 2 boxes × 5 meters/box = 10 meters
New scale:
- Length = 15 meters ÷ 20 meters/box = 0.75 boxes
- Width = 10 meters ÷ 20 meters/box = 0.5 boxes
Continuing this way for other examples, we find:
The drawing that appears to be consistent with the calculations for 1 box = 20 meters would be the one that displays dimensions compatible with this basis.
Based on the images described:
- The first rectangle (2 units long and 1 unit wide) would represent 40 meters long and 20 meters wide which is consistent.
- The second rectangle (3 units long and 2 units wide) corresponds to 60 meters long and 40 meters wide which is also consistent.
- The third rectangle (6 units long and 3 units wide), represents 120 meters long and 60 meters wide.
Since we have different possible dimensions but need the corresponding ones, the best response regarding keeping the proportions similar in new scale derived from the original scale would be:
The image with the rectangle drawn on it that is 3 units long and 2 units wide, labeled with 3 and 2 respectively.