Question

if the area of a rombus is 216cm² and one of its diagnol measures 24 cm . find the other diagnol of the rhombus​

Answer 1

the area of a rhombous = (1/2)* product of diagonals

let other diagonal be d

(1/2)*24*d = 216

d = 216/12

d = 18 cm

Answer 2

Answer:

Area of rhombus= 1/2×d1×d2

⇒216= 1/2×24×d2

⇒216=12×d2

⇒ 216/12 =d2

⇒d2=18cm

So, second diagonal =18cm

As shown in fig. AC=18CM,BD=24CM

Since, diagonals of rhombus bisects each other at right angle.

∴AO=9cm,DO=12cm

In △AOD

AO² +DO² =AD²

⇒9²+12² =AD²

⇒81+144=AD²

⇒225=AD²

⇒AD=15cm

∴ side of rhombus (AD)=15cm

Perimeter of rhombus =4×side

=4×15=60cm

Perimeter of rhombus =60cm