The Correct Answer and Explanation is:
The correct answer is 1 cm : 6 m.
Here is a detailed explanation of how to determine the scale of the drawing.
The problem asks for the scale of a drawing, which is a ratio that connects the measurements on the drawing to the actual measurements of the object. A scale is typically expressed in its simplest form, showing what one unit on the drawing represents in reality.
First, we must identify the given information. We know the length of the playground in the scale drawing is 12 centimeters. We also know the actual length of the real playground is 72 meters. The width of the drawing is given as 8 centimeters, but we do not need this information to find the scale, as the length measurements provide a complete pair of corresponding values.
To find the scale, we set up a ratio of the drawing’s length to the actual length. This initial ratio is 12 cm to 72 m, which we can write as 12 cm : 72 m.
However, scales are most useful when they are simplified. The standard convention is to simplify the ratio so that the drawing’s measurement is 1 unit. To achieve this, we need to find a number that we can divide both parts of the ratio by to make the first number 1. In this case, we can divide both sides of the ratio by 12.
Let’s perform the calculation.
For the drawing measurement: 12 cm ÷ 12 = 1 cm.
For the actual measurement: 72 m ÷ 12 = 6 m.
After simplifying, we get the new ratio of 1 cm : 6 m. This is the final scale of the drawing. It clearly states that every 1 centimeter of length on the paper represents 6 meters of length in the actual playground. This result matches one of the provided options.
