In a ΔABC, DE || BC, where D is a point on AB and E is a…

In a ΔABC, DE || BC, where D is a point on AB and E is a point on AC. If DE divides the area of ΔABC into two equal parts, then DB : AB is equal to:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. √2 - 1 : √2.

Given that

DE divides the area of ΔABC into two equal parts

Area of ΔABC = 2 × Area of ΔADE

AB = AD + DB

According to the question

Area of ΔABC/Area of ΔADE = (AB²/AD²)

2 × Area of ΔADE/Area of ΔADE = (AB²/AD²)

⇒ (AB²/AD²) = 2

⇒ AB/AD = $\sqrt2$

⇒ AB = $\sqrt2$ AD

⇒ AB = $\sqrt2$ (AB - DB)

⇒ DB $\sqrt2$ = ( $\sqrt2$ - 1) AB

⇒ DB/AB = ( $\sqrt2$ - 1)/ $\sqrt2$

SSC CGL 2023 PYQ — Question 65