In the given figure, AE = 5 cm and EC = 7 cm, then area of △ ADE : area of △ ABC is :

1. 5 : 7

2. 7 : 5

3. 25 : 144

4. 144 : 25

From figure,

In △ ADE and △ ABC,

⇒ ∠DAE = ∠BAC (Common angle)

⇒ ∠ADE = ∠ABC (Corresponding angles are equal)

∴ △ ADE ~ △ ABC (By A.A. postulate)

From figure,

AC = AE + EC = 5 + 7 = 12 cm.

We know that,

The areas of two similar triangles are proportional to the squares on their corresponding sides.

$\therefore \dfrac{\text{Area of △ ADE}}{\text{Area of △ ABC}} = \dfrac{AE^2}{AC^2} \\[1em] = \dfrac{5^2}{12^2} \\[1em] = \dfrac{25}{144} \\[1em] = 25 : 144.$

Hence, Option 3 is the correct option.