Answer: The correct option is
(B) Yes, the sides are in the ratio 2:5.
Step-by-step explanation: We are given to check whether the triangles can be similar based on the side lengths alone.
From the figure, we note that
the sides lengths of the triangle RST are
RS = 3.0 cm, ST = 6.0 cm and RT = 6.4 cm.
and the corresponding side lengths of triangle XUW are
XU = 7.5 cm, UW = 15.0 cm and XW = 16.0 cm.
So, the ratio of the corresponding sides of the two triangles are as follows :
[tex]\dfrac{RS}{XU}=\dfrac{3}{7.5}=\dfrac{30}{75}=\dfrac{2}{5},\\\\\\\dfrac{ST}{UW}=\dfrac{6}{15}=\dfrac{2}{5},\\\\\\\dfrac{RT}{XW}=\dfrac{6.4}{16}=\dfrac{64}{160}=\dfrac{2}{5}.[/tex]
Therefore, we get
[tex]\dfrac{RS}{XU}=\dfrac{ST}{UW}=\dfrac{RT}{XW}=\dfrac{2}{5}=2:5.[/tex]
Hence, the corresponding sides are proportional and they are in the ratio 2 : 5.
Thus, (B) is the correct option.
