Question

On the blueprint of a house, 35 millimeters represents 10 meters. The actual length of the living room is 9 meters. What is its length on the blueprint?

Answer 1

The length of the living room on the blueprint is found by setting up the proportion 35 mm / 10 m = x mm / 9 m, and solving for x to get 31.5 millimeters. This is done by cross-multiplication and unit conversion.

Step-by-step explanation:

To calculate the length of the living room on the blueprint, we need to set up a proportion using the scale provided. The scale says that 35 millimeters represent 10 meters in actual length. We can write this as a ratio: 35 mm / 10 m = x mm / 9 m, where x is the length we want to find on the blueprint.

First, we cross-multiply to solve for x:

1. 35 mm × 9 m = 10 m × x mm
2. 315 mm² = 10 m × x mm
3. Since mm² and m are not the same units, we need to convert 315 mm² into square meters or convert 10 m into millimeters before we divide.
4. As 1 m = 1000 mm, 10 m will be 10000 mm. Now we have:
5. 315 mm = 10000 mm × x
6. x = 315 mm / 10000 mm = 0.0315 m (on the blueprint)
7. To get the answer in millimeters, we convert it back: 0.0315 m × 1000 = 31.5 mm

The actual length of the living room, which is 9 meters, would be represented by 31.5 millimeters on the blueprint.