Compare the side in triangle $ABC$ whose length you know ($AB$) with the corresponding side in triangle $DEF$ ($DE$). What ratio does this give you?

Once you know how much longer triangle $DEF$ is compared to triangle $ABC$, multiply the side in $ABC$ that corresponds to $EF$ (that is, $BC$) by this same factor.

In an expression line, type $(10/6)*9$ and evaluate it. The resulting value is the length of $EF$, which should match one of the answer choices.

From the statement, $A \leftrightarrow D$, $B \leftrightarrow E$, and $C \leftrightarrow F$, so side $AB$ corresponds to $DE$ and side $BC$ corresponds to $EF$.

Use these corresponding sides to set up a proportion:

• $AB = 6$ corresponds to $DE = 10$
• $BC = 9$ corresponds to $EF$

So the ratio of corresponding sides must be equal:

$\dfrac{DE}{AB} = \dfrac{EF}{BC}$, which is $\dfrac{10}{6} = \dfrac{EF}{9}$.

Start with the proportion:

Use cross multiplication to solve for $EF$:

90 = 6 \cdot EF

EF = \dfrac{90}{6}

Simplify $\dfrac{90}{6}$:

So the length of $\overline{EF}$ is $15$, which corresponds to answer choice C.