Question

If the diagonal of a rhombus are 18 cm and 24 cm respectively, then its side is equal to......
(Find using Pythagoras theorem -Remember that diagonals of a rhombus bisect each other at right angles). Single choice.

Answer 1

Question :-

If the diagonal of a rhombus are 18 cm and 24 cm respectively, then its side is equal to......

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,

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

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

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

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

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

$AD = 15cm$

Hence the all side of rhombus are equal

Hence the each side of the rhombus is 15cm.

Answer 2

Given: The length of the diagonals of a rhombus are 18 cm and 24 cm.

To find: Length of each side

Solution: The sides of a rhombus are equal to each other.

Let the rhombus be denoted by abcd. Let the diagonal ac and bd intersect at a point o.

Let ac= 18 cm and bd= 24 cm

The diagonals of a rhombus bisect each other at right angles.

Therefore, ao= oc= 9 cm

ob = od = 12 cm

In triangle aob, ao= 9 cm, ob= 12 cm and ab= Length of the side of rhombus

${(ab)}^{2} = {(ao)}^{2} + {(ob)}^{2}$

$= > {(ab)}^{2} = {(9)}^{2} + {(12)}^{2}$

$= > {(ab)}^{2} = 81 + 144$

$= > {(ab)}^{2} = 225$

=>ab= ✓225

=>ab= 15 cm

Therefore, the length of each side of the rhombus is 15 cm.