Question

Trisha measured a swimming pool and made a scale drawing. She used the scale 8 centimeters = 2 meters. What scale factor does the drawing use? Simplify your answer and write it as a ratio, using a colon.

A. 1:2
B. 1:4
C. 2:1
D. 4:1

Answer 1

To calculate the scale factor, the given scale of 8 centimeters to 2 meters must be converted into the same units, resulting in a scale factor of 1:25. A similar example demonstrates that when converting a scale of 3 inches to 12 feet into the same unit (inches), the scale factor is 1:48.

Step-by-step explanation:

To calculate the scale factor used in Trisha's drawing of a swimming pool, we first need to convert the given scale of 8 centimeters = 2 meters into a consistent unit of measure. Since 1 meter is equal to 100 centimeters, 2 meters is equal to 200 centimeters. Now, we can express the scale as the ratio of drawing distance to the actual distance in the same units:

8 cm (drawing) / 200 cm (actual) = 1/25

This ratio can be expressed as the scale factor of the drawing, which is 1:25, simplifying the fraction 1/25 into the ratio form.

Now, let's answer a similar scale factor question.

For a scale factor of 3 inches to 12 feet, we convert 12 feet into inches since there are 12 inches in a foot:

12 feet * 12 inches/foot = 144 inches

Now, write the ratio of the scale drawing to the actual size:

3 inches (drawing) / 144 inches (actual) = 1/48

Thus, the scale factor is 1:48.