In triangle ABC, D is a point on BC such that BD : DC = 3…

In triangle ABC, D is a point on BC such that BD : DC = 3 : 4. E is a point on AD such that AE " ED = 2 : 3. Find the ratio area (ΔECD) : area (ΔAEB).

Show answer & explanation

Correct answer: B

Explanation

The correct answer is Option 2. i.e. 2 : 1.

As one knows that the line from vertex (cevian) cuts the opposite side in a certain ratio then the area of two new triangles is also divided in that ratio.

Area of $\triangle$ BED : Area of $\triangle$ EDC = 3 : 4.......(1)

Area of $\triangle$ BED : Area of $\triangle$ AEB = 3 : 2......(2)

On combining both the equation we get,

Area of $\triangle$ BED : Area of $\triangle$ EDC : Area of $\triangle$ AEB = 3 : 4 : 2.

Now Area of $\triangle$ EDC : Area of $\triangle$ AEB = 4 : 2 = 2 : 1.

SSC CGL 2021 PYQ — Question 71