Question

Your teacher will give you a scale drawing of a basketball court. The drawing does not have any measurements labeled, but it says that 1 centimeter represents 2 meters. Measure the distances on the scale drawing that are labeled a–d to the nearest tenth of a centimeter. Record your results in the first row of the table. The statement "1 cm represents 2 m" is the scale of the drawing. It can also be expressed as "1 cm to 2 m," or "1 cm for every 2 m." What do you think the scale tells us? How long would each measurement from the first question be on an actual basketball court? Explain or show your reasoning.

a. Measurement (a): 3.5cm.
b. Measurement (b): 6.2cm.
c. Measurement (c): 13.7cm.
d. Measurement (d):18.4cm.

Answer 1

The scale on a drawing indicates the ratio between the drawing's measurements and the actual measurements. By multiplying the drawing measurements by the scale factor (1 cm = 2 m), actual distances can be calculated for the basketball court, yielding 7 m, 12.4 m, 27.4 m, and 36.8 m respectively for distances a to d.

Step-by-step explanation:

The scale on a drawing tells us the relationship between the measurements on the drawing and the actual measurements. To find the actual measurement, you multiply the drawing measurement by the scale factor. In the given question, the scale is 1 cm = 2 m.

Here's how to calculate the actual measurements for each labeled distance:

• Measurement (a): 3.5 cm on the drawing is 3.5 * 2 m = 7 m on the actual basketball court.
  
• Measurement (b): 6.2 cm on the drawing is 6.2 * 2 m = 12.4 m on the actual basketball court.
  
• Measurement (c): 13.7 cm on the drawing is 13.7 * 2 m = 27.4 m on the actual basketball court.
  
• Measurement (d): 18.4 cm on the drawing is 18.4 * 2 m = 36.8 m on the actual basketball court.

Applying this concept to other problems, we can say:

• A meeting room that is 1.5 cm by 2.5 cm on a scale drawing with a scale of 1 cm to 2 meters would have an actual area of (1.5 * 2) * (2.5 * 2) = 3 m * 5 m = 15 m².
• Samir ran a 10-kilometer race; 1 kilometer is 1000 meters, so Samir ran 10 * 1000 m = 10,000 meters.
• For a scale model with a height of 1.5 meters where the scale is 1 cm = 0.5 m, the actual building would have a height of 1.5 / 0.5 = 3 meters.

The conversion of metric units of measurement is straightforward because the metric system is based on powers of 10. For instance, there are 100 centimeters in a meter, so to convert meters to centimeters, we multiply by 100. Hence, 3.55 meters equals 355 centimeters.