#SSC CGL

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Question : If $\Delta$ PQR and $\Delta$ LMN are similar and 3PQ = LM and MN = 9, then QR is equal to:
Option 1: 9 cm
Option 2: 6 cm
Option 3: 12 cm
Option 4: 3 cm

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Team Careers360 9th Jan, 2024

Answer (1)

Team Careers360 15th Jan, 2024

Correct Answer: 3 cm

Solution : The corresponding sides of two similar triangles are in equal proportion.
$\Delta$ PQR $\sim\Delta$ LMN
$⇒\frac{\mathrm{PQ}}{\mathrm{LM}} = \frac{\mathrm{QR}}{\mathrm{MN}} = \frac{\mathrm{PR}}{\mathrm{LN}}$
$⇒\frac{\mathrm{PQ}}{\mathrm{LM}} = \frac{QR}{\mathrm{MN}}\\$
$⇒\frac{1}{3} = \frac{\mathrm{QR}}{9\;\mathrm{cm}}\\$
$⇒\mathrm{QR} = 3\;\mathrm{cm}$
Hence, the correct answer is 3 cm.

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