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Question
Each side of a rhombus is 10 cm. If one of its diagonals is 16 cm find the length of the other diagonal.
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
AO2 + BO2 = AB2
⇒ AO2 + 82 = 102
⇒ AO2 = 100 − 64 = 36
⇒ AO = `sqrt36` = 6 cm [By above property]
Hence, AC = 6 + 6 = 12 cm
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