Question

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

Answer 1

Answer:

the correct answer is c

Step-by-stepth explanation:

Answer 2

Answer:

Q1:   The correct option is:   16

Q2:   The correct options are: $\frac{AB}{DE}=\frac{AC}{DF}$ and $\frac{AC}{DF}=\frac{BC}{EF}$

Q3:   The correct option is:  $\overline{BC}=12; \overline{EF}=16$

Step-by-step explanation:

Question 1:

As here  $\triangle RST\sim \triangle MNO$, so the ratio of the corresponding sides will be equal. That means.....

$\frac{RS}{MN}=\frac{RT}{MO}\\ \\ \frac{8}{x}=\frac{6.5}{13}\\ \\ 6.5x=8*13\\ \\ x=\frac{8*13}{6.5}=16$

So, the length of the side $x$ 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............

$\frac{AB}{DE}=\frac{1}{3} \\ \\ \frac{BC}{EF}=\frac{2}{6}=\frac{1}{3}\\ \\ \frac{AC}{DF}=\frac{2}{7}$

So we can see that the ratio of side $AC$ and side $DF$ is not equal with the other ratios.

Thus, the proportions that show the triangles are not similar:  $\frac{AB}{DE}=\frac{AC}{DF}$ and $\frac{AC}{DF}=\frac{BC}{EF}$

Question 3:

Given that,  $\frac{AB}{DE}=\frac{BC}{EF}$  

The ratio of $AB$ and $DE$ is given as $\frac{3}{4}$

So, the ratio of $BC$ and $EF$ will be also $\frac{3}{4}$

Among the four options, if $BC=12$ and $EF=16$, only then the ratio will be $\frac{3}{4}$

$\frac{BC}{EF} =\frac{12}{16}= \frac{3}{4}$

So, the lengths of $BC$ and $EF$ could be 12 and 16 respectively.