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SSC CHSL 2024 PYQ — Question 62

SSC CHSL - 03 July 2024 - Shift 4 • Quantitative Aptitude • Q62

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∆ABC ~ ∆EDF and area (∆ABC) : area (∆EDF) = 9 : 4. If AB = 5 cm, BC = 8 cm and CA = 10 cm, then DF is equal to:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 513cm5 \frac{1}{3} \rm cm.

Given:

∆ABC ~ ∆EDF

Area(∆ABC) : Area(∆EDF) = 9 : 4

AB = 5 cm, BC = 8 cm, CA = 10 cm

To find: DF

When two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides. 

So, (Area(∆ABC) / Area(∆EDF)) = (AB/DE)2^2 = (BC/DF)2^2 = (CA/EF)2^2

Given, (Area(∆ABC) / Area(∆EDF)) = 9/4

Therefore, (BC/DF)2^2 = 9/4

Taking the square root of both sides:

BC/DF = 3/2

Substituting the value of BC:

⇒ 8/DF = 3/2

⇒ 3 × DF = 8 × 2

⇒ DF = 16/3 cm

Therefore, DF is equal to 16/3 cm.