Triangle $ABC$ has sides $8\text{ cm}$, $12\text{ cm}$ and $15\text{ cm}$. Triangle $DEF$ is similar to $ABC$ and has two sides of $4\text{ cm}$ and $6\text{ cm}$. Find the length of the third side of $DEF$.

Step-by-step solution

1. Find the similarity ratio using the corresponding sides: $\frac{4}{8}=\frac{1}{2}$.
2. Apply the same ratio to the third side: $\frac{x}{15}=\frac{1}{2}$.
3. Solve for $x$: $x=15\times \frac{1}{2}=7.5$ cm.
4. The third side of $DEF$ measures $7.5$ cm.

Concept tested: Similarity of triangles

Published 4 October 2026 · How this solution was prepared and checked