SarkariPYQ

SSC Selection Post 2019 PYQ — Question 52

SSC Selection Post - Higher Secondary Level - 16 Oct 2019 - Shift 2 • Quantitative Aptitude • Q52

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Let ΔABC ~ ΔPQR and ar(△ABC)ar(△QPR)=9169{ar(\bigtriangleup ABC) \over ar(\bigtriangleup QPR)} = {9\over169}. If AB = 12 cm, BC = 7 cm and AC = 8 cm, then PQ (in cm) is equal to:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 52.

Given, ΔABC ~ ΔPQR

⇒ ar(△ABC)ar(△QPR)=(ABPQ)2=(BCQR)2=(ACPR)2{ar(\bigtriangleup ABC) \over ar(\bigtriangleup QPR)} = (\frac{AB}{PQ})^2 = (\frac{BC}{QR})^2 = (\frac{AC}{PR})^2

Now, AC = 12 cm, then

⇒ 9169=(12PQ)2\frac{9}{169} = (\frac{12}{PQ})^2

⇒ 12/PQ = 3/13

⇒ PQ = 52 cm