Question

if the diagonal of a rhoumbos are 18 cm and 24 cm respectively, then it's side is equal to?
​

Answer 1

Step-by-step explanation:

Required Answer :-

Hence the each side of the rhombus is 15cm.

Explanation :-

Let the rhombus is ABCD, given that :

AC=24cm and BD=18cm.

Let the Diagonal of Rhombus bisect each other at right angles.

AO=OC= 12

and OB = OD =9 cm

Let ∠AOD=90°

In right ΔAOD,

AO= 12 cm and OD=9 cm

By using phythagoras theorem,

{AD}^{2} = {AO}^{2} + {OD}^{2}AD

2

=AO

2

+OD

2

{AD}^{2} = {(12)}^{2} + {(9)}^{2}AD

2

=(12)

2

+(9)

2

{AD}^{2} = 144 + 81AD

2

=144+81

{AD}^{2} = {(225)}^{2}AD

2

=(225)

2

{AD}^{2} = {(15)}^{2}AD

2

=(15)

2

AD = 15cmAD=15cm

Hence the all side of rhombus are equal

Hence the each side of the rhombus is 15cm.