The side lengths of triangle ABC

Question

are 10, 14, and 16. The side lengths of triangle A′B′C′
are 35, 49, and 56. Identify the scale factor of a single dilation between the preimage ABC
and image A′B′C′
.(1 point)
Responses

27
Start Fraction 2 over 7 End Fraction

3
3

5.6
5.6

3.5

Answer 1

To find the scale factor of the dilation between triangles \( ABC \) and \( A'B'C' \), we can compare corresponding side lengths.

1. The side lengths of triangle \( ABC \) are 10, 14, and 16.
2. The side lengths of triangle \( A'B'C' \) are 35, 49, and 56.

We can calculate the scale factor by dividing the side lengths of triangle \( A'B'C' \) by the corresponding side lengths of triangle \( ABC \):

For the side of length 10 in triangle \( ABC \): \[ \text{Scale factor} = \frac{35}{10} = 3.5 \]

For the side of length 14 in triangle \( ABC \): \[ \text{Scale factor} = \frac{49}{14} = 3.5 \]

For the side of length 16 in triangle \( ABC \): \[ \text{Scale factor} = \frac{56}{16} = 3.5 \]

In all cases, the scale factor is \( 3.5 \).

Thus, the scale factor of the dilation is \( \boxed{3.5} \).