M is a point on side AB of rectangle ABCD. If AD = 3 cm, DM = 5 cm and CM = 3√5 cm, then find the length of AB.

Option 1 : 10 cm

**Given:**

ABCD is a rectangle

AD = 3 cm

DM = 5 cm

CM = 3√5 cm

**Concept used:**

Using the concept of Pythagoras theorem, i.e.,

Base^{2} + Height^{2} = Hypotenous^{2}

**Calculation:**

In triangle AMD,

By using Pythagoras Theorem

AD^{2} + AM^{2} = DM^{2}

⇒ 3^{2} + AM^{2} = 5^{2}

⇒ AM^{2} = 16

⇒ AM = 4 cm …..(1)

In triangle BCM,

By using Pythagoras Theorem

BC^{2} + BM^{2} = CM^{2}

⇒ 3^{2} + BM^{2} = (3√5)^{2} [BC = AD]

⇒ BM^{2} = 36

⇒ BM = 6 cm …..(2)

AB = AM + BM

⇒ AB = 4 + 6 [From using (1) and (2)]

⇒ AB = 10 cm

**∴**** The length of AB is 10 cm.**