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,

h^{2} = p^{2} + b^{2}

10^{2} = 6^{2} + AO^{2}

⇒ 100 = 36 + AO^{2}

⇒ AO^{2} = 100 – 36

⇒ AO^{2} = 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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