A scale is a ratio that compares the size of an object in a drawing to its actual size in real life. The notation 1 centimeter colon 5 meters means that every 1 centimeter on the drawing represents 5 meters in reality.
To convert real measurements to scale drawings, we set up a proportion. If 1 centimeter represents 5 meters, then x centimeters represent 12 meters. We can solve this by cross multiplying: 1 times 12 equals 5 times x, which gives us 12 equals 5x.
Now let's solve the equation step by step. Starting with 1 fifth equals x over 12, we cross multiply to get 5x equals 1 times 12, which simplifies to 5x equals 12. Dividing both sides by 5 gives us x equals 12 fifths, which equals 2.4. Therefore, a 12-meter room is represented by 2.4 centimeters on the scale drawing.
To verify our solution, let's visualize both the real room and its scale representation. The real room is 12 meters long, shown on the left. Its scale representation is 2.4 centimeters, shown on the right. The ruler demonstrates how 2.4 centimeters on the drawing corresponds to the full length of the room in reality, confirming our calculation is correct according to the 1 centimeter to 5 meters scale ratio.
Let's practice with two more examples using the same 1 centimeter to 5 meters scale. Example 1: A garden is 20 meters long. To find its scale length, we set up the proportion 1 centimeter over 5 meters equals x centimeters over 20 meters. Cross multiplying gives us 5x equals 20, so x equals 4 centimeters. Example 2: A wall measures 3 centimeters on the scale drawing. To find its real length, we set up the proportion 1 centimeter over 5 meters equals 3 centimeters over x meters. Cross multiplying gives us 1 times x equals 3 times 5, so x equals 15 meters. These examples show that the same scale conversion method works in both directions.