Scale is a ratio that compares the size of an object in a drawing to its actual size. In this case, the scale 1 centimeter to 6 meters means that every 1 centimeter on the drawing represents 6 meters in real life.
We can express the scale as a ratio to make calculations easier. The scale 1 centimeter to 6 meters can be written as the fraction 1 cm over 6 m. We are given that the actual room length is 13 meters.
To find the drawing length, we set up a proportion using the scale ratio. We have 1 centimeter over 6 meters equals x centimeters over 13 meters, where x is the unknown drawing length for the 13-meter actual length.
To solve the proportion, we cross-multiply. This gives us 1 times 13 equals 6 times x. Simplifying, we get 13 equals 6x. Finally, dividing both sides by 6, we find that x equals 13 over 6.
Let's convert the improper fraction 13 over 6 to a mixed number and decimal for practical use. 13 divided by 6 equals 2 with a remainder of 1, so we get 2 and 1 sixth. As a decimal, this is approximately 2.17. To verify, if 2.17 centimeters represents 13 meters, then 1 centimeter should represent about 6 meters. Multiplying 2.17 by 6 gives us 13.02 meters, which confirms our answer is correct.
Let's visualize the difference between the scale drawing and the actual room. The scale drawing of our 13-meter room would be only 2.17 centimeters long. For comparison, I've shown a line representing the actual 13-meter length. This dramatic difference shows how scale allows us to represent large objects on a manageable drawing.
Let's apply the same method to find the drawing length of a 9-meter wall. We set up the proportion: 1 over 6 equals x over 9. Cross-multiplying gives us 1 times 9 equals 6 times x. This simplifies to 9 equals 6x. Dividing both sides by 6, we find x equals 9 over 6, which is 1.5 centimeters.