Question
Triangles ABC and XYZ are similar figures, because angles A, B, and C are congruent to angles X, Y, and Z, respectively.
If side AC equals 5 cm, BC equals 9 cm, and XZ equals 25 cm, what is the length of side YZ?
A.
55 cm
B.
35 cm
C.
45 cm
D.
36 cm
If side AC equals 5 cm, BC equals 9 cm, and XZ equals 25 cm, what is the length of side YZ?
A.
55 cm
B.
35 cm
C.
45 cm
D.
36 cm
Answers
GPT 3.5
To find the length of side YZ, we need to find the scale factor between the two triangles ABC and XYZ.
The scale factor can be found by comparing the corresponding sides of the two triangles.
In triangle ABC, the ratio of side lengths is:
AC/XY = 5/25 = 1/5
Now, we can use this scale factor to find the length of side YZ:
YZ = BC * scale factor
YZ = 9 * 1/5
YZ = 9/5
YZ = 1.8 * 10 = 18 cm
Therefore, the length of side YZ is 18 cm.
Answer: Not listed on the options.
The scale factor can be found by comparing the corresponding sides of the two triangles.
In triangle ABC, the ratio of side lengths is:
AC/XY = 5/25 = 1/5
Now, we can use this scale factor to find the length of side YZ:
YZ = BC * scale factor
YZ = 9 * 1/5
YZ = 9/5
YZ = 1.8 * 10 = 18 cm
Therefore, the length of side YZ is 18 cm.
Answer: Not listed on the options.
pick the answer from the list please and pick it correctly
GPT 3.5
Apologies for the mistake in the previous explanation. Let's correct it:
To find the length of side YZ, we can set up a proportion using the sides of the two triangles:
AC/XY = BC/YZ
Substitute the given lengths:
5/25 = 9/YZ
Cross multiply:
5YZ = 225
YZ = 45 cm
Therefore, the length of side YZ is 45 cm.
Answer: C. 45 cm
To find the length of side YZ, we can set up a proportion using the sides of the two triangles:
AC/XY = BC/YZ
Substitute the given lengths:
5/25 = 9/YZ
Cross multiply:
5YZ = 225
YZ = 45 cm
Therefore, the length of side YZ is 45 cm.
Answer: C. 45 cm