ABC EDF and ar ABC ar DEF 4 9 If AB 6 cm BC 8 cm and AC 10 cm then DF is equal to ........

Quantitative Aptitude (CGL) Geometry

$\bigtriangleup$ ABC $\sim \bigtriangleup$ EDF and ar( $\bigtriangleup$ ABC) : ar( $\bigtriangleup$ DEF) = 4 : 9. If AB = 6 cm, BC = 8 cm and AC = 10 cm,then DF is equal to

This questions was previously asked in

SSC CGL 12 June 2019 Shift-3

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9 cm

12 cm

15 cm

18 cm

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Explanation:

We have
ABC similar to EDF
Now ratio of areas of similar triangles = (Square of ratio of sides )
Therefore we can say
The ratio of sides of ABC and EDF will be $\sqrt{_{9}^{4}} = _{3}^{2}$
Now we get
BC : DF = 2:3
Substituting we get DF = 12