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?

Question

(1 point)
Responses

113
1 Start Fraction 1 over 3 End Fraction

2
2

123
1 Start Fraction 2 over 3 End Fraction

12 .

Answer 1

To determine the scale factor used to create the copy of the triangle, we need to compare the lengths of corresponding sides of the two triangles.

Let's say the length of a side in the original triangle is \( a \) cm and the length of the corresponding side in the new triangle is \( b \) cm.

The scale factor can be calculated using the formula:

\[ \text{Scale Factor} = \frac{\text{Length of side in new triangle}}{\text{Length of side in original triangle}} = \frac{b}{a} \]

Without specific measurements for the side lengths of the triangles, it's challenging to calculate a precise scale factor.

If we fill in hypothetical values:

1. If the original triangle has a side of length 3 cm and the new triangle has a side of length 2 cm, the scale factor would be:

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

2. If the original triangle has a side of length 1 cm and the new triangle has a side of length 1 cm, the scale factor would be:

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

3. If the original triangle has a side of length 3 cm and the new triangle has a side of length 6 cm, the scale factor would be:

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

You will need to measure the sides of the triangles and apply the above formula to determine the exact scale factor among the provided options:

• \( 1 \frac{1}{3} \)
• \( \frac{1}{3} \)
• \( 2 \)
• \( \frac{2}{3} \)
• 1

Please provide the side lengths or additional context for further assistance in determining the correct scale factor.

Answer 2

10 in
15 in
18 in

36 in
20 in
30 in

Answer 3

To determine the scale factor between the two triangles based on the provided side lengths, we will compare the corresponding sides.

Original Triangle Side Lengths:

• 10 in
• 15 in
• 18 in

Copy Triangle Side Lengths:

• 36 in
• 20 in
• 30 in

Next, we'll calculate the scale factor for each corresponding side:

1. For the first pair of sides (10 in to 36 in): \[ \text{Scale Factor} = \frac{36}{10} = 3.6 \]

2. For the second pair of sides (15 in to 20 in): \[ \text{Scale Factor} = \frac{20}{15} = \frac{4}{3} \approx 1.33 \]

3. For the third pair of sides (18 in to 30 in): \[ \text{Scale Factor} = \frac{30}{18} = \frac{5}{3} \approx 1.67 \]

Since the scale factors for corresponding sides are not consistent, there is no uniform scale factor between these two triangles.

To find the overall scale factor, you would typically expect all corresponding sides to have the same scale factor. However, given that these ratios differ, the triangles are not similar.

If the question is asking for a specific scale factor, the best possible answer based on the closest ratio among your options might be:

• If you were looking for a uniform scale factor among typical choices (as many problems assume similarity), then you'd point out that they do not have a consistent scale factor, and you may clarify that none of the provided options fit.

If you'd like more help, please let me know!