Question

find tr
s
e f
11
t r
a. 5.5
b. 11
c. 22
d. 33

Explanation:

Step1: Identify similar - triangles

Since $\frac{SE}{ST}=\frac{SF}{SR}$ and $\angle S$ is common, $\triangle SEF\sim\triangle STR$ by the Side - Angle - Side (SAS) similarity criterion.

Step2: Determine the similarity ratio

The marks on the sides show that $\frac{SE}{ST}=\frac{1}{2}$.

Step3: Use the similarity ratio for side - length

If $\triangle SEF\sim\triangle STR$, then the ratio of their corresponding sides is the same. Let the length of $EF = 11$ and the length of $TR$ be $x$. The ratio of corresponding sides is $\frac{EF}{TR}=\frac{SE}{ST}$. Since $\frac{SE}{ST}=\frac{1}{2}$, we have $\frac{11}{x}=\frac{1}{2}$.

Step4: Solve for $TR$

Cross - multiply: $x = 22$.

Answer:

C. 22