Let $\triangle ABC \sim \triangle RPQ$ and $\frac{ar(\triangle ABC)}{ar(\triangle PQR)} = \frac{4}{9}$. If AB = 3 cm, BC = 4 cm and AC = 5 cm, then PQ (in cm) is equal to:

6

As Triangle ABC is similar to triangle RPQ

\(\frac{AB}{RP}\) = \(\frac{BC}{PQ}\) = \(\frac{AC}{QR}\) = √(\(\frac{ar(ABC)}{ar(RPQ)}\))

Calculation

\(\frac{BC}{PQ}\) = √(\(\frac{4)}{9}\))

= \(\frac{4}{PQ}\) = (\(\frac{2}{3}\))

= PQ = 6 cm.

Therefore, PQ is 6 cm.