If $ riangle ABC \sim riangle PQR$ in which $AB = 6$ cm, $BC = 4$ cm, $AC = 8$ cm and $PR = 6$ cm, then find the length of $(PQ + QR)$.

Question

If $	riangle ABC \sim 	riangle PQR$ in which $AB = 6$ cm, $BC = 4$ cm, $AC = 8$ cm and $PR = 6$ cm, then find the length of $(PQ + QR)$.

Accepted Answer

Step 1: Since $	riangle ABC \sim 	riangle PQR$: $\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$, i.e., $\frac{6}{PQ} = \frac{4}{QR} = \frac{8}{6}$
Step 2: $PQ = \frac{6 	imes 6}{8} = \frac{9}{2} = 4.5$ cm and $QR = \frac{4 	imes 6}{8} = 3$ cm
Step 3: $	herefore PQ + QR = 4.5 + 3 = 7.5$ cm

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