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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.

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Answer:

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.

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