please help i will be the happiest person alive 100 points and branliest

Answer:Q1:   The correct option is:   16Q2:   The correct options are: [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]Q3:   The correct option is:  [tex]\overline{BC}=12; \overline{EF}=16[/tex]Step-by-step explanation:Question 1:As here  [tex]\triangle RST\sim \triangle MNO[/tex], so the ratio of the corresponding sides will be equal. That means.....[tex]\frac{RS}{MN}=\frac{RT}{MO}\\ \\ \frac{8}{x}=\frac{6.5}{13}\\ \\ 6.5x=8*13\\ \\ x=\frac{8*13}{6.5}=16[/tex]So, the length of the side [tex]x[/tex] will be 16.Question 2:If two triangles are similar, then the ratio of their corresponding sides should be equal.  So, here the ratios of the corresponding sides are............[tex]\frac{AB}{DE}=\frac{1}{3} \\ \\ \frac{BC}{EF}=\frac{2}{6}=\frac{1}{3}\\ \\ \frac{AC}{DF}=\frac{2}{7}[/tex]So we can see that the ratio of side [tex]AC[/tex] and side [tex]DF[/tex] is not equal with the other ratios. Thus, the proportions that show the triangles are not similar:  [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]Question 3:Given that,  [tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]  The ratio of [tex]AB[/tex] and [tex]DE[/tex] is given as [tex]\frac{3}{4}[/tex]So, the ratio of [tex]BC[/tex] and [tex]EF[/tex] will be also [tex]\frac{3}{4}[/tex]Among the four options, if [tex]BC=12[/tex] and [tex]EF=16[/tex], only then the ratio will be [tex]\frac{3}{4}[/tex][tex]\frac{BC}{EF} =\frac{12}{16}= \frac{3}{4}[/tex]So, the lengths of [tex]BC[/tex] and [tex]EF[/tex] could be 12 and 16 respectively.