To determine the correct scale for the playground when the original drawing is scaled down from a scale of 1 box = 5 meters to a scale of 1 box = 20 meters, we need to see how the dimensions of the playground should be adjusted.
Original dimensions of the playground: \( 8 , \text{boxes} \times 4 , \text{boxes} \)
Since the original scale is 1 box = 5 meters, the real size of the playground is:
- Width: \( 8 \times 5 = 40 , \text{meters} \)
- Length: \( 4 \times 5 = 20 , \text{meters} \)
Now, we need to convert these dimensions to fit the new scale (1 box = 20 meters):
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Width in new scale: \[ \text{Width} = \frac{40 , \text{meters}}{20 , \text{meters/box}} = 2 , \text{boxes} \]
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Length in new scale: \[ \text{Length} = \frac{20 , \text{meters}}{20 , \text{meters/box}} = 1 , \text{box} \]
The new dimensions for the playground at the scale of 1 box = 20 meters will be \( 2 , \text{boxes} \times 1 , \text{box} \).
Looking at the options provided: a. 3 x 2 b. 6 x 3 c. 2 x 1 d. 16 x 8
The correct scale is c. 2 x 1.