Question

Scale: 1 box = 5 meters

Reproduce the scale drawing 8 x 4 of a playground so that it has a scale of 1 box = 20 meters
which is the correct scale?
a. 3 x 2
b. 6 x 3
c. 2 x 1
d. 16 x 8

Answer 1

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):

1. Width in new scale:
\[ \text{Width} = \frac{40 \, \text{meters}}{20 \, \text{meters/box}} = 2 \, \text{boxes} \]

2. 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**.