Question

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

Explanation:

Step1: Identify similar - triangles

Since $SE = ET$ and $SF=FR$, by the mid - point theorem for triangles, $\triangle SEF\sim\triangle STR$. The ratio of their sides is $1:2$ because $E$ and $F$ are mid - points of $ST$ and $SR$ respectively.

Step2: Use the ratio of corresponding sides

The ratio of the side lengths of similar triangles is constant. If the length of $EF = 11$, and $\frac{EF}{TR}=\frac{SE}{ST}=\frac{1}{2}$. Then $TR = 2\times EF$.

Step3: Calculate the length of $TR$

Substitute $EF = 11$ into the formula $TR = 2\times EF$. So $TR=2\times11 = 22$.

Answer:

C. 22