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WBCS Preliminary Examination 2023 — General Studies · Question 115 of 200

Q115
ArithmeticRatio, Proportion & Mixtures
The perimeter of a triangle whose sides are in the ratio $\dfrac{1}{20}:\dfrac{1}{15}:\dfrac{1}{12}$ is 30 cms. The length of the biggest side is
  1. a.$7\dfrac{1}{2}$ cms
  2. b.10 cms
  3. c.$12\dfrac{1}{2}$ cms
  4. d.7 cms

Answer: (C) $12\dfrac{1}{2}$ cms

Multiply the ratio $\dfrac{1}{20}:\dfrac{1}{15}:\dfrac{1}{12}$ by 60, the LCM of the denominators, to get $3:4:5$. The sum of the ratio terms is 12 and the perimeter is 30 cm, so one part is $30\div12=2.5$ cm. The sides are therefore 7.5 cm, 10 cm and 12.5 cm, and the longest is $12\dfrac{1}{2}$ cm. Options (A) and (B) are the other two sides. Since $3:4:5$ is a Pythagorean triple, this is a right-angled triangle. Remember that the largest fraction, $\dfrac{1}{12}$, corresponds to the longest side.

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