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SSC CGL 2019 PYQ — Question 56

SSC CGL - 4th June 2019 - Shift 1 • Quantitative Aptitude • Q56

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In ΔABC, F and E are the points on sides AB and AC, respectively, such that FE||BC and FE divides the triangle in two parts of equal area. If AD ⊥ BC and AD intersects FE at G,Find GD : AG.

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Correct answer: D

Explanation

Correct answer is option 4 i.e. (√2 – 1) : 1

Concept

Understanding

Application

If all three angles of 2 triangles are equal, then these two triangles are similar triangles.

And

(Area of triangle1/ Area of triangle2) = (Side12/Side22)

Given that: FE|| BC, then all 3 angles of triangles ABC and AFE will be equal.

So, triangle ABC is similar to triangle AFE.

 

And FE divides area of triangle ABC equally:

Area of ABC/Area of AFE = 2/1

 

 

(Area of ABC/ Area of AFE) = AD2/AG2

⇒ 2/1 = AD2/AG2

⇒ AD/AG = √2/1

 

Hence, AD = √2 and AG = 1

Then GD = √2 - 1

GD : AG = (√2 – 1) : 1