Answer :

Given: Side of rhombus = 10 cm


Length of one diagonal = 12 cm


The figure for the question is:



We know that diagonals a rhombus are perpendicular bisector to each other.


So, the ΔAOB is a right angled triangles with AOB as right angle.


Now, in ΔAOB,


h = 10 cm


p = 6 cm


b = AO


By applying Pythagoras Theorem we have,


h2 = p2 + b2


102 = 62 + AO2


100 = 36 + AO2


AO2 = 100 – 36


AO2 = 64


AO = √64 = 8 cm


Also,


OD = AO = 1/2AD [ Diagonals of rhombus bisect each other]


AD = 2 × AO


AD = 2 × 8


AD = 16 cm


Thus the length of the other diagonal is 16 cm.


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