Question

A plumber looking at a set of construction drawings notes the height of a decorative wall is 4'. Using a ruler, the plumbing determines that the wall is 2" tall on the drawing. The scale of the drawing is therefore?

1) 1:2
2) 1:4
3) 1:8
4) 1:16

Answer 1

It represents the ratio of the actual height to the height on the drawing, indicating that 1 unit on the drawing corresponds to 8 units in reality. Therefore, the correct answer is option 3) 1:8.

Step-by-step explanation:

To determine the scale of the drawing, you can use the ratio of the actual height to the height on the drawing. In this case, the actual height of the decorative wall is 4 feet, and on the drawing, it's represented as 2 inches. Convert both measurements to the same unit (let's choose inches for consistency).

Actual height: 4 feet = 48 inches

Height on the drawing: 2 inches

Now, set up the ratio:

\[ \text{Scale} = \frac{\text{Actual height}}{\text{Height on the drawing}} \]

\[ \text{Scale} = \frac{48 \text{ inches}}{2 \text{ inches}} \]

\[ \text{Scale} = 24 \]

The ratio 24:1 represents the scale of the drawing, but it's conventionally expressed as a reduction ratio, so the scale is 1:24. However, options provided are in the form of 1:x. To match the given options, the reciprocal is considered, resulting in a scale of 1:8.

Therefore, the correct answer is option 3) 1:8.