Each side of a rhombus is 10 cm and one of its diagonals is 16 cm, length of other diagonal will be :
11 cm
12 cm
13 cm
15 cm

Question

Each side of a rhombus is 10 cm and one of its diagonals is 16 cm, length of other diagonal will be : 1. 11 cm 2. 12 cm 3. 13 cm 4. 15 cm

KnowledgeBoat · Accepted Answer

Let ABCD be the rhombus and the diagonals intersect at point O.

Let diagonal AC = 16 cm.

We know that,

Diagonals of rhombus bisect each other at right angles.

∴ AO = OC = $\dfrac{AC}{2} = \dfrac{16}{2}$ = 8 cm and BO = OD = x cm (let).

In right angle triangle AOB,

By pythagoras theorem,

⇒ (Hypotenuse)² = (Perpendicular)² + Base²

⇒ AB² = AO² + OB²

⇒ 10² = 8² + x²

⇒ 100 = 64 + x²

⇒ x² = 100 - 64

⇒ x² = 36

⇒ x = $\sqrt{36}$ = 6 cm.

From figure,

⇒ BD = BO + OD = 6 + 6 = 12 cm.

Hence, option 2 is the correct option.

Mathematics