If AE = 10 cm, BD = 8 cm and BC = 10 cm, then AB is equal to :

1. 5 cm

2. 25 cm

3. 12.5 cm

4. 2.5 cm

From figure,

In △ ACE and △ BCD,

⇒ ∠CAE = ∠CBD (Both equal to 90°)

⇒ ∠ACE = ∠BCD (Common angles)

Since, two angles of two triangles are equal so third angle of both the triangle will also be equal.

⇒ ∠CEA = ∠CDB.

∴ △ ACE ~ △ BCD (By A.A.A. postulate)

We know that,

Corresponding sides of similar triangle are in proportion.

$\therefore \dfrac{AC}{BC} = \dfrac{AE}{BD} \\[1em] \Rightarrow \dfrac{AC}{10} = \dfrac{10}{8} \\[1em] \Rightarrow AC = \dfrac{100}{8} = 12.5 \text{ cm}.$

From figure,

AB = AC - BC = 12.5 - 10 = 2.5 cm.

Hence, Option 4 is the correct option.