What is the scale factor for the similar triangles? Choose all that apply.

Question

Similar triangles; larger triangle has side lengths 2 and 8; smaller triangles has corresponding side lengths 1.5 and 6

Multiple select question.

1/2


2/3


3/4


2


3/2


4/3

Answer 1

To find the scale factor for the similar triangles, we can divide the side lengths of the larger triangle by the corresponding side lengths of the smaller triangle.

For the larger triangle with side lengths of 2 and 8, and the smaller triangle with corresponding side lengths of 1.5 and 6:

1. First side: \[ \text{Scale factor} = \frac{\text{larger triangle side}}{\text{smaller triangle side}} = \frac{2}{1.5} = \frac{2 \times 2}{1.5 \times 2} = \frac{4}{3} \]

2. Second side: \[ \text{Scale factor} = \frac{8}{6} = \frac{8 \div 2}{6 \div 2} = \frac{4}{3} \]

Both sides yield the same scale factor of \( \frac{4}{3} \).

Now, let's check which options correspond to this scale factor of \( \frac{4}{3} \):

• 1/2: Not applicable
• 2/3: Not applicable
• 3/4: Not applicable
• 2: Not applicable
• 3/2: Not applicable
• 4/3: Applicable

The only applicable answer for the scale factor is:

• 4/3

Answer 2

what if it was getting bigger

Answer 3

If the triangles are similar and the larger triangle is scaling up, the scale factor will still be calculated the same way, by taking the ratio of corresponding sides. However, when the larger triangle's sides are compared to the smaller triangle's sides, the scale factor will be greater than 1.

Given the same side lengths as before:

• Larger triangle sides: 2 and 8
• Smaller triangle sides: 1.5 and 6

To find the scale factor from the smaller triangle to the larger triangle, you do the following:

1. First side: \[ \text{Scale factor} = \frac{\text{larger triangle side}}{\text{smaller triangle side}} = \frac{2}{1.5} = \frac{2 \times 2}{1.5 \times 2} = \frac{4}{3} \]

2. Second side: \[ \text{Scale factor} = \frac{8}{6} = \frac{8 \div 2}{6 \div 2} = \frac{4}{3} \]

Since both calculations yield a scale factor of \( \frac{4}{3} \), this means that if the smaller triangle is scaled up to match the larger triangle, the scale factor is \( \frac{4}{3} \).

While the scale factor is \( \frac{4}{3} \) when increasing from the smaller triangle to the larger one, it is still referred to the same as before; it simply denotes that the larger triangle is \( \frac{4}{3} \) times the size of the smaller triangle.

Therefore, given that the triangles are getting bigger, the only applicable scale factor remains:

• 4/3

Just as a note, a scale factor greater than 1 indicates enlargement. Any applicable values from your previous options indicating the scale factor of enlargement should include \( \frac{4}{3} \). The other values you provided would remain invalid for this case.