Question

Find the value of $x$ if $\Delta ABC\sim \Delta PQR$.

• A. $4cm$
• B. ${30}^{\circ }$
• C. $8cm$

Answer 1

Two triangles are similar if their corresponding angles are equal and corresponding sides are in the same ratio.

Given that $\Delta ABC\sim \Delta PQR$.


From the property of similar triangles,
$\frac{AB}{PQ}=\frac{BC}{QR}\to \frac{8}{x}=\frac{6}{3}\to x=4cm$


From the property of similar triangles,
$\angle P=\angle A\to x=30°$



From the property of similar triangles,
$\frac{BC}{QR}=\frac{AC}{PR}\to \frac{x}{6}=\frac{8}{6}\to x=8cm$