Question

The area of a rhombus is 234 cm². If its one diagonal is 18 cm, find the lengths of its side and the other diagonal. Also, find perimeter of the rhombus.

Answer 1

Area of a rhombus = 234cm²
Length of one diagonal = d₁ = 18cm
Let the side of rhombus be 'a' cm and length of other diagonal be d₂ cm.

Now, area of rhombus = `(1)/(2) xx "Product of diagonal"`

⇒ 243 = `(1)/(2) xx "d"_1 xx "d"_2`

234 = `(1)/(2) xx 18 xx "d"_2`

⇒ 234 = 9 x d₂

⇒ d₂ = `(234)/(9)`
= 26cm
Now,

(Side)² = `("d"/2)^2 + ("d"_2/2)^2`

= `(18/2)^2 + (26/2)^2`

= 81 + 169
= 250
⇒ Side = `5sqrt(10)"cm"`
Hence, perimeter of a rhombus
= 4 x Side
= `4 xx 5sqrt(10)`
= `20sqrt(10)"cm"`.