Answer: [tex]\triangle RST\sim \triangle UVW[/tex]; [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
If In two triangles,
Two pairs of sides of two triangles are in same ratio and there are congruent angle between them,
Then By SAS similarity postulate the triangles are similar.
Here In triangles RST and UVW, (According to the given figure)
[tex]\frac{RS}{UV} = \frac{10}{12} = \frac{5}{6}[/tex]
And, [tex]\frac{TR}{WU} = \frac{15}{18} = \frac{5}{6}[/tex]
Thus, [tex]\frac{RS}{UV}=\frac{TR}{WU}[/tex]
Also, [tex]\angle U\cong \angle R = 32^{\circ}[/tex]
Thus, by SAS similarity postulate,
[tex]\triangle RST\sim \triangle UVW[/tex]
Also, the scale factor or common ratio is [tex]\frac{5}{6}[/tex]
Thus, First Option is correct.
