Question
If ΔPQR and ΔLMN are similar and 3PQ = LM and MN = 9 cm, then QR is equal to:
Answer: Option D
$$\eqalign{
& \frac{{PQ}}{{LM}} = \frac{{QR}}{{MN}} = \frac{{PR}}{{LN}} \cr
& \left( {\vartriangle PQR\,{\text{and}}\,\vartriangle LMN\,{\text{are}}\,{\text{similar}}} \right) \cr
& \frac{{PQ}}{{LM}} = \frac{{QR}}{{MN}} \cr
& \frac{1}{3} = \frac{{QR}}{9} \cr
& QR = 3\,{\text{cm}} \cr} $$
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$$\eqalign{
& \frac{{PQ}}{{LM}} = \frac{{QR}}{{MN}} = \frac{{PR}}{{LN}} \cr
& \left( {\vartriangle PQR\,{\text{and}}\,\vartriangle LMN\,{\text{are}}\,{\text{similar}}} \right) \cr
& \frac{{PQ}}{{LM}} = \frac{{QR}}{{MN}} \cr
& \frac{1}{3} = \frac{{QR}}{9} \cr
& QR = 3\,{\text{cm}} \cr} $$
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