Question

7. Consider the similar trianges below.

Part A:
The first triangle is, S, 5, 7, R, 8, T and the second triangle is, B, 14, C, A.
Find the scale factor.
The scale factor is: ____
Part B
Find the length of AC.
The length of AC is ____

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the scale factor, we can compare corresponding sides of the triangles.

In the first triangle, SR = 5 and RT = 8.
In the second triangle, BC = 14, so the corresponding side must be 5 * (14/8) = 8.75.

Therefore, the scale factor is 8.75.

To find the length of AC, we use the scale factor.

In the first triangle, ST = 7.
Since the scale factor is 8.75, the corresponding side in the second triangle must be 7 * 8.75 = 61.25.

Therefore, the length of AC is 61.25.

Answer 2

7. Consider the similar trianges below.

Part A:
The first triangle is, S, 5, 7, R, 8, T and the second triangle is, B, 14, C, A.
Find the scale factor.
The scale factor is: ____ (has to be a whole number)
Part B
Find the length of AC.
The length of AC is ____ (has to be a whole number)

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the scale factor, we can compare the corresponding sides of the triangles.

In the first triangle, SR = 5 and RT = 8.
In the second triangle, BC = 14. To find the corresponding side, we can set up a proportion:

SR/RT = BC/AC
5/8 = 14/AC

Cross multiplying, we get:
5 * AC = 8 * 14
5AC = 112
AC = 112/5 = 22.4

Since the scale factor has to be a whole number, we can round 22.4 to the nearest whole number, which is 22.

Therefore, the scale factor is 22.

To find the length of AC, we use the scale factor.

In the first triangle, ST = 7.
Since the scale factor is 22, the corresponding side in the second triangle must be 7 * 22 = 154.

Therefore, the length of AC is 154.