Answer
$13.5$ units
Work Step by Step
Step 1: Since the triangles are similar, their corresponding sides are in
proportion.
Step 2: This means that $\frac{9}{x}=\frac{16}{24}$.
Step 3: Solving through cross multiplication: $16x=24\times9$.
Step 4: $16x=216$.
Step 5: $x=\frac{216}{16}=\frac{27}{2}= 13.5$ units.
Check:
Step 1: Equating the two proportions to see if they reduce to the same fraction: $\frac{16}{24}=\frac{9}{\frac{27}{2}}$.
Step 2: Simplifying both sides: $\frac{16}{24}=\frac{9\times2}{27}$.
Step 3: $\frac{16}{24}=\frac{18}{27}$.
Step 4: $\frac{2}{3}=\frac{2}{3}$.
Step 5: Therefore, the answer is accurate.
