Question
Figure STUV and figure WXYZ, shown below, are similar figures.
The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 117 mm and SV = 153 mm, what is the length of side WX?
A.
459 mm
B.
51 mm
C.
39 mm
D.
351 mm
The scale factor of figure STUV to figure WXYZ is 3:1. If ST = 117 mm and SV = 153 mm, what is the length of side WX?
A.
459 mm
B.
51 mm
C.
39 mm
D.
351 mm
Answers
GPT-4o mini
Since figures STUV and WXYZ are similar and the scale factor from STUV to WXYZ is 3:1, it means that each side of figure STUV is 3 times the corresponding side of figure WXYZ.
Given that \( ST = 117 \, \text{mm} \), we can use the scale factor to find the corresponding side WX in figure WXYZ.
To find WX, we can set up the relationship based on the scale factor:
\[
\text{E} = \frac{\text{Length of ST}}{\text{Scale Factor}} = \frac{117 \, \text{mm}}{3} = 39 \, \text{mm}
\]
Thus, the length of side \( WX \) is \( 39 \, \text{mm} \).
The correct answer is:
C. 39 mm
Given that \( ST = 117 \, \text{mm} \), we can use the scale factor to find the corresponding side WX in figure WXYZ.
To find WX, we can set up the relationship based on the scale factor:
\[
\text{E} = \frac{\text{Length of ST}}{\text{Scale Factor}} = \frac{117 \, \text{mm}}{3} = 39 \, \text{mm}
\]
Thus, the length of side \( WX \) is \( 39 \, \text{mm} \).
The correct answer is:
C. 39 mm