Each side of rhombus is 13 cm and one of its diagonals is 10 cm. Find :

(i) the length of its other diagonal

(ii) its area.

(i) Given :

AB = 13 cm

AC = 10 cm

Then, OA = OC = $\dfrac{10}{2}$ = 5 cm

Since the diagonals of a rhombus bisect at 90°.

Applying pythagoras theorem in triangle AOB, we get:

AB² = OA² + OB²

⇒ (13)² = (5)² + OB²

⇒ 169 = 25 + OB²

⇒ OB² = 169 - 25

⇒ OB² = 144

⇒ OB = $\sqrt{144}$

⇒ OB = 12

BD = 2 x OB

= 2 x 12 cm

= 24 cm

Hence, the length of other diagonal is 24 cm.

(ii) As we know, the area of rhombus = $\dfrac{1}{2}$ x product of its diagonal

= $\dfrac{1}{2}$ x 10 x 24 cm²

= $\dfrac{1}{2}$ x 240 cm²

= 120 cm²

Hence, the area of the rhombus is 120 cm².