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SSC CGL 2021 PYQ — Question 62

SSC CGL - 20 Aug 2021 - Shift 1 • Quantitative Aptitude • Q62

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In Δ\Delta ABC, D is a point on side AB such that BD = 3 cm and DA = 4 cm. E is a point on BC such that DE || AC, Then Area of Δ\Delta BDE : Area of trapezium ACED = 

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 9 : 40.

Triangle BDE is similar to triangle ABC (DE || AC)

One knows that the area of similar triangles will be equal to the square of the ratio of their corresponding sides.

△BDE△ABC\frac{ \triangle BDE}{ \triangle ABC} = (BD)2/(AB)2 

⇒ △BDE△ABC\frac{ \triangle BDE}{ \triangle ABC}= 9/49

⇒ Area of Δ\Delta BDE : Area of trapezium ACED = 9 : 49 - 9 = 9 : 40