Because $DE$ is parallel to $BC$, the smaller triangle $ADE$ and the larger triangle $ABC$ are similar. Think about which sides in the small triangle match which sides in the big triangle.

Match $AD$ with $AB$ and $AE$ with $AC$. Write a fraction with $AD$ and $AB$ on one side and $AE$ and $AC$ on the other, then solve for $AC$.

When you solve the proportion, you will need to either simplify a fraction or divide using decimals. Work carefully or use a calculator so you don’t lose accuracy.

In Desmos, type the expression 5.4*8/4.8 (this corresponds to $AC = AE \cdot AB / AD$ using the similar-triangles proportion) and look at the numeric result that Desmos gives; that value is the length of $AC$.

Point $D$ is on side $\overline{AB}$, and you are told $AD = 4.8$ and $DB = 3.2$.

So the full length of side $AB$ is the sum of these two parts:

Compute this sum to get the length of $AB$.

Segment $DE$ is drawn parallel to side $\overline{BC}$ of $\triangle ABC$, with $D$ on $AB$ and $E$ on $AC$.

When a segment inside a triangle is parallel to one side and touches the other two sides, it creates a smaller triangle similar to the original triangle.

So $\triangle ADE \sim \triangle ABC$.

That means the ratios of corresponding sides are equal:

• $AD$ corresponds to $AB$
• $AE$ corresponds to $AC$

So you can write a proportion involving $AD$, $AB$, $AE$, and $AC$.

From the similarity $\triangle ADE \sim \triangle ABC$ and the matching sides, use the ratio

You know $AD = 4.8$, $AB$ from Step 1, and $AE = 5.4$. Plug these numbers into the proportion.

You will get an equation of the form

Now solve the equation from Step 3 for $AC$.

First, simplify the fraction on the left using your value for $AB$ to get a decimal (a simple proportion like $0.6$).

Then you will have an equation like

Divide both sides by that decimal to isolate $AC$:

Carrying out this division gives $AC = 9$, so the correct answer is choice B.