Question

luka was given an enlargement of a wooden block.

which statements about the original figure and its enlargement are true? select three options.

the scale factor of this enlargement is 2.

the scale factor of this enlargement is \\( \frac { 1 } { 2 } \\).

the length of side a can be found by multiplying 24 mm by the scale factor.

the length of side a can be found by dividing 24 mm by the scale factor.

the length of side a is 12 mm.

Explanation:

Step1: Calculate the scale factor

The original height is 8 mm and the enlarged height is 16 mm. The scale factor \( k \) is calculated as \( \frac{\text{Enlarged length}}{\text{Original length}} = \frac{16}{8} = 2 \). So the scale factor of this enlargement is 2.

Step2: Determine how to find side A

The enlarged base is 24 mm. Since the scale factor is 2 (enlargement), to find the original length (side A), we multiply the enlarged length by the reciprocal of the scale factor (or divide by the scale factor). But since the scale factor from original to enlarged is 2, to get original from enlarged, we do \( \text{Original length} = \frac{\text{Enlarged length}}{\text{Scale factor}} \)? Wait, no. Wait, original to enlarged: original scale factor = enlarged. So original = enlarged / scale factor. Wait, no: if original is 8, scale factor 2, enlarged is 16 (82=16). For the base: original (A) * 2 = 24, so A = 24 / 2 = 12. So to find A, we can multiply 24 by (1/scale factor) or divide 24 by scale factor. But let's check the options:

Option 1: Scale factor is 2. Correct, as 16/8=2.

Option 3: Length of A can be found by multiplying 24 by scale factor? 24*2=48, which is not A. So no.

Option 4: Length of A can be found by dividing 24 by scale factor. 24/2=12, which is A. Correct.

Option 5: Length of A is 12 mm. 24/2=12, correct.

Wait, let's re-express:

Scale factor (enlargement) is 2 (since 82=16). So original (A) 2 = 24 => A = 24 / 2 = 12. So:

• The scale factor of this enlargement is 2: Correct.

• The length of side A can be found by multiplying 24 mm by the scale factor: 24*2=48≠12, so incorrect.

• The length of side A can be found by dividing 24 mm by the scale factor: 24/2=12, correct.

• The length of side A is 12 mm: Correct.

Wait, the options are:

1. The scale factor of this enlargement is 2. (Correct)

1. The scale factor of this enlargement is \( \frac{1}{2} \). (Incorrect, since 16/8=2)

1. The length of side A can be found by multiplying 24 mm by the scale factor. (Incorrect, 24*2=48≠A)

1. The length of side A can be found by dividing 24 mm by the scale factor. (Correct, 24/2=12)

1. The length of side A is 12 mm. (Correct, 24/2=12)

So the three true options are:

• The scale factor of this enlargement is 2.

• The length of side A can be found by dividing 24 mm by the scale factor.

• The length of side A is 12 mm.

Answer:

The three true statements are:

• The scale factor of this enlargement is 2.
• The length of side A can be found by dividing 24 mm by the scale factor.
• The length of side A is 12 mm.

(In boxed form for the options, assuming the options are labeled as follows:

1. The scale factor of this enlargement is 2.
2. The scale factor of this enlargement is \( \frac{1}{2} \).
3. The length of side A can be found by multiplying 24 mm by the scale factor.
4. The length of side A can be found by dividing 24 mm by the scale factor.
5. The length of side A is 12 mm.

Then the correct options are 1, 4, 5.)

So the three correct options are:

1. The scale factor of this enlargement is 2.
2. The length of side A can be found by dividing 24 mm by the scale factor.
3. The length of side A is 12 mm.