Question

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

विकल्प

• 5 cm

• 25 cm

• 12.5 cm

• 2.5 cm

Answer 1

If AE = 10 cm, BD = 8 cm and BC = 10 cm, then AB is equal to 2.5 cm.

Explanation:

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.

∴ `(AC)/(BC) ​= (AE)/(BD)​`

⇒ `(AC)/10 ​= 10/8`

⇒ AC = `= 100/8​ = 12.5 cm`

From figure,

AB = AC − BC = 12.5 − 10 = 2.5 cm.