ABC EDF and ar ABC ar DEF 1 4 If AB 7cm BC 8 cm and CA 9 cm then DF is equal to ........

Quantitative Aptitude (CGL) Geometry

$\bigtriangleup$ ABC $\sim \bigtriangleup$ EDF and ar( $\bigtriangleup$ ABC): ar( $\bigtriangleup$ DEF) = 1 : 4. If AB = 7cm, BC = 8 cm and CA = 9 cm, then DF is equal to:

This questions was previously asked in

SSC CGL 13 June 2019 Shift-1

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8 cm

16 cm

18 cm

14 cm

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Explanation:

Theorem: If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their
corresponding sides. This proves that the ratio of areas of two similar triangles is proportional to the squares of the corresponding
sides of both the triangles.
Since $\bigtriangleup$ ABC $\sim \bigtriangleup$ EDF ,
$$\frac{area of triangle$$ABC}{area of triange EDF} = \frac{BC^2}{DF^2}$$
$$\frac{1}{2} = \frac{8}{DF}$$
DF = 16 cm
So , the answer would be option b)16 cm.

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