Each side of a rhombus is 10 cm. If one of its diagonals is 16 cm find the length of the other diagonal.

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#### Solution

We have,

ABCD is a rhombus with side 10 cm and diagonal BD = 16 cm

We know that diagonals of a rhombus bisect each other at 90°

∴ BO = OD = 8 cm

In ΔAOB, by pythagoras theorem

AO^{2} + BO^{2} = AB^{2}

⇒ AO^{2} + 8^{2} = 10^{2}

⇒ AO^{2} = 100 − 64 = 36

⇒ AO = `sqrt36` = 6 cm [By above property]

Hence, AC = 6 + 6 = 12 cm

Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle

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