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SSC Selection Post 2022 PYQ — Question 71

SSC Selection Post - Higher Secondary Level 2022 - 10 Feb 2022 - Shift 2 • Quantitative Aptitude • Q71

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Let △ABC ~ △PQR and area(△ABC)area(△PQR)area(△ABC)\over{area(△PQR)}= 2514425\over144.If AB = 12 cm, BC = 7 cm and AC = 9 cm, then PR (in cm) is equal to:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 21.6.

The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.

Area of (△ABC)Area of (△PQR)=(ACPR)2 \frac{\text{Area of } (\triangle ABC)}{\text{Area of } (\triangle PQR)} = \left( \frac{AC}{PR} \right)^2

⇒25144=(ACPR)2\Rightarrow \frac{25}{144} = \left( \frac{AC}{PR} \right)^2

⇒25144=(9PR)2\Rightarrow \frac{25}{144} = \left( \frac{9}{PR} \right)^2

PR = 9 ×  12/5 = 21.6