Question

answer me please because I unable to understand this question in my board exam​

Answer 1

Given: DE || BC, AD = 2cm, BD = 3cm.

To find: ar(ΔABC) : ar(ΔADE)

Answer:

According to basic proportionality theorem, if a line is drawn || to one side of triangle to intersect other two sides, then other two sides are divided in the same ratio.

$\frac{AD}{AB} = \frac{AE}{AC}$

$\frac{2}{3+2} = \frac{AE}{AC}$

$\frac{2}{5} = \frac{AE}{AC}$

∴ ar(ΔABC) : ar(ΔADE) = (AC:AE)²

= 5² / 2²

= 25 / 4

∴ The answer is d) 25:4