Ask a New Question
Menu

A board game uses a triangular piece measuring 3 inches on each side. The travel version of the game uses a triangle in a proportional relationship to the original. It measures 0.5 inches on each side. Identify the scale factor used to create the travel version of the piece.(1 point)

Responses:

3.5
Start Fraction 1 over 6 End Fraction
6
−1/6

5 answers

To find the scale factor used to create the travel version of the piece, we can compare the side lengths of the original triangle to the side lengths of the travel version.

The original triangle measures 3 inches on each side, and the travel version measures 0.5 inches on each side.

The scale factor can be calculated using the formula:

\[ \text{Scale Factor} = \frac{\text{Length of Travel Version}}{\text{Length of Original Version}} = \frac{0.5}{3} \]

Calculating this gives:

\[ \text{Scale Factor} = \frac{0.5}{3} = \frac{1}{6} \]

So, the scale factor used to create the travel version of the piece is:

Start Fraction 1 over 6 End Fraction.

Randee draws these two triangles with lengths given in centimeters. What scale factor does she use to create the copy on the right from the original on the left?

(1 point)
Responses
1 1/3

2

1 2/3

1/2

To determine the scale factor that Randee used to create the copy of the triangle on the right from the original triangle on the left, we need to compare the lengths of corresponding sides of the two triangles.

Let’s denote the length of a side of the original triangle as \( L_{original} \) and the length of the corresponding side of the copied triangle as \( L_{copy} \).

The scale factor can be calculated using the formula:

\[ \text{Scale Factor} = \frac{L_{copy}}{L_{original}} \]

Without the specific lengths given for the triangles, I can provide you with an example process if you have the lengths:

  1. If the original triangle has a side length of 6 cm and the copy has a side length of 4 cm, the scale factor would be:

\[ \text{Scale Factor} = \frac{4}{6} = \frac{2}{3} \]

  1. If the original triangle has a side length of 3 cm and the copy has a side length of 4 cm, the scale factor would be:

\[ \text{Scale Factor} = \frac{4}{3} = 1 \frac{1}{3} \]

Please provide the lengths of the sides of both triangles to calculate the exact scale factor, or use the provided example process with your specific numbers!

The first triangle lengths are: 10,15,and 18
Second triangle lengths are: 36,30,and 20

To find the scale factor Randee used to create the copy on the right (the second triangle) from the original on the left (the first triangle), we can compare the lengths of corresponding sides.

The lengths of the triangles are:

  • First triangle (original): 10 cm, 15 cm, 18 cm
  • Second triangle (copy): 36 cm, 30 cm, 20 cm

Next, we can find the scale factor using the formula:

\[ \text{Scale Factor} = \frac{L_{copy}}{L_{original}} \]

We can calculate the scale factor for each pair of corresponding sides:

  1. For the sides 10 cm (original) and 36 cm (copy): \[ \text{Scale Factor} = \frac{36}{10} = 3.6 \]

  2. For the sides 15 cm (original) and 30 cm (copy): \[ \text{Scale Factor} = \frac{30}{15} = 2 \]

  3. For the sides 18 cm (original) and 20 cm (copy): \[ \text{Scale Factor} = \frac{20}{18} = \frac{10}{9} \approx 1.11 \]

Since the scale factor should be consistent across corresponding sides of similar triangles, this indicates that the triangles are not proportionally similar across all sides.

The scale factor from the original triangle to the second triangle varies between the sides. However, if the goal is to identify one common scale factor, we can take the most applicable scale from the provided options, which is 2 (based on the second pair of sides).

Thus, the scale factor Randee used to create the copy on the right is 2.