Two triangles $PQR$ and $XYZ$ are similar. Triangle $PQR$ has sides $7$, $21$ and $28$ cm. Triangle $XYZ$ is similar to $PQR$ and has side $XY=14$ cm. Find all the sides of triangle $XYZ$ and its perimeter.

Step-by-step solution

1. Since the triangles are similar, the ratios of corresponding sides are equal.
2. Let the similarity ratio be $k$ such that $XY=k\times 7$.
3. Given $XY=14$ cm, solve for $k$: $14=k\times 7$ implies $k=\frac{14}{7}=2$.
4. Apply the same ratio to the other two sides of $PQR$. $YZ=k\times 21=2\times 21=42$ cm. $ZX=k\times 28=2\times 28=56$ cm.
5. Now compute the perimeter of $XYZ$ by adding its sides: $14+42+56=112$ cm.
6. Thus $XYZ$ has sides $14$ cm, $42$ cm, $56$ cm and its perimeter is $112$ cm.

Concept tested: Similarity of triangles

Published 10 October 2026 · How this solution was prepared and checked