Multiple choice

A right angled (\triangle ABC) is 90° at B. Given that BC = 5 cm and AB = 12 cm. If (\triangle ABC) is similar to (\triangle PQR) and 4AC = PR, then find area of (\triangle PQR).

  1. $480cm2$
  2. $500 cm2$
  3. $520 cm2$
  4. $180 cm2$
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A Correct answer
Explanation

Find AC using Pythagoras: AC = √(12² + 5²) = 13 cm. Since triangles are similar, 4AC = PR means scale factor = PR/AC = 4. Area scales by the square of the scale factor: Area(PQR) = 4² × Area(ABC) = 16 × (1/2 × 12 × 5) = 16 × 30 = 480 cm².

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