If the length of a diagonal of a rhombus is 30 cm and its area is 240 sq cm, find its perimeter.

we know that,

Given that area of rhombus = 240 sq cm

And diagonal BD = 30cm

⇒other diagonal, AC = 240 × 2 ÷ 30

AC = 16cm

We know that diagonals of a rhombus bisect each other,

So let E be the midpoint of their point of intersection.

Now, AE = 16/2 = 8cm

And BE = 30/2 = 15cm

Now, ∆ABE is right angle triangle

∴ using Pythagoras theorem,

AE²+ BE² = AB²

⇒AB = 17cm

We know that perimeter of rhombus = 4 × side of rhombus

= 4 × 17

= 68 cm