The perimeter of a rhombus is 60 cm. If one of its diagonals is 18 cm long, find (i) the length of the other diagonal, and (ii) the area of the rhombus.
Given:
Perimeter of rhombus = 60 cm
Length of diagonal 1 (d1) = 18 cm
Let, Length of diagonal 2 be d2
(i) Perimeter of rhombus = 4 × side
⇒ 60 = 4 × side
Now,
Side of rhombus = 1/2 × √(d12 + d22)
⇒ 15 = 1/2 × √(182 + d22)
⇒ 15 = 1/2 × √(324 + d22)
⇒ 15 × 2 = √(324 + d22)
⇒ 30 = √(324 + d22)
Squaring both sides,
⇒ 900 = 324 + d22
⇒ 900-324 = d22
⇒ d22 = 576
⇒ d2 = 24
Therefore,
Length of other diagonal = 24 cm
(ii) Area of rhombus = 1/2 × d1 × d2
= 1/2 × 18 cm × 24 cm
= 216 cm2