Question

question 6 (1 point) if the figures below are similar, find the scale factor of figure b to figure a scale factor: ____ blank 1:

Explanation:

Step1: Identify corresponding sides

First, we need to match the corresponding sides of the similar triangles. Let's list the side lengths:

• Figure A: 27, 48, 60
• Figure B: 9, 16, 20

We can see that 9 corresponds to 27, 16 corresponds to 48, and 20 corresponds to 60.

Step2: Calculate scale factor

The scale factor from Figure B to Figure A is the ratio of a side length of B to the corresponding side length of A. Let's take one pair, say 9 (from B) and 27 (from A):
Scale factor = $\frac{\text{Side of B}}{\text{Side of A}} = \frac{9}{27} = \frac{1}{3}$? Wait, no, wait. Wait, the problem says "scale factor of Figure B to Figure A". Wait, no, let's check again. Wait, maybe I mixed up. Wait, let's check the sides:

Wait, 9 (B) and 27 (A): 9/27 = 1/3

16 (B) and 48 (A): 16/48 = 1/3

20 (B) and 60 (A): 20/60 = 1/3

Wait, so the scale factor of B to A is 1/3? Wait, no, wait. Wait, scale factor from B to A is (length of B)/(length of A). So yes, 9/27 = 1/3, 16/48 = 1/3, 20/60 = 1/3. So the scale factor is 1/3? Wait, but let's confirm.

Wait, maybe I made a mistake. Wait, let's check the sides again. Let's see:

Figure A: 27, 48, 60

Figure B: 9, 16, 20

So 9 is 1/3 of 27, 16 is 1/3 of 48, 20 is 1/3 of 60. So the scale factor from B to A is 1/3? Wait, no, wait. Wait, scale factor is (new length)/(original length). If we are going from B to A, then A is the larger one, so B is the smaller. So the scale factor is (length of B)/(length of A) = 9/27 = 1/3.

Wait, but let's check again. Let's take 16 (B) and 48 (A): 16/48 = 1/3. 20 (B) and 60 (A): 20/60 = 1/3. So yes, the scale factor is 1/3.

Wait, but let me confirm. The scale factor from B to A is (side of B)/(side of A) = 9/27 = 1/3. So that's the scale factor.

Answer:

$\frac{1}{3}$