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SSC CHSL 2024 PYQ — Question 57

SSC CHSL - 05 July 2024 - Shift 1 • Quantitative Aptitude • Q57

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∆ABC is similar to ∆DEF, and the ratio of the area of triangle ABC to triangle DEF is 25 ∶ 144. If AB = p cm, AC = q cm, and BC = r cm, then DE =?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 125p\frac{12}{5}p.

(Area of ∆ABC)/(Area of ∆DEF) = 25/144

⇒ (AB/DE)2 = (AC/DF)2 = (BC/EF)2 = 25/144

⇒ AB/DE = AC/DF = BC/EF = 5/12

AB = p

So, p/DE = 5/12

⇒ DE = (12p)/5

⇒ DE = (12/5)p

Therefore, the value of DE is (12/5)p.