Question

A triangle ABC with sides AB = 6 cm, BC = 12 cm and AC = 8 em is enlarged to $△$PQR such that its largest side is 18 cm. Find the ratio and hence find the lengths of theremaining sides of $△$PQR

• A. $\frac{2}{3}$, PQ $=$11 cm, PR $=$5 cm.
• B. $\frac{2}{3}$, PQ $=$7 cm, PR $=$17 cm.
• C. $\frac{2}{3}$, PQ $=$2 cm, PR $=$11 cm.
• D. $\frac{2}{3}$, PQ $=$9 cm, PR $=$12 cm.

Answer 1

The correct option is D $\frac{2}{3}$, PQ $=$9 cm, PR $=$12 cm.

Since, $△ABC$ is enlarged to $△PQR$
hence, $△ABC\sim △PQR$
or ratio of sides = $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$
ratio of sides = $\frac{6}{PQ}=\frac{12}{18}=\frac{8}{PR}$
ratio of sides = $\frac{2}{3}$
and $PQ=9$ cm and $PR=12$ cm