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Question
Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.
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Solution
Side of the rhombus = 10cm
One diagonal, d1 = 16cm
Let d2 be the other diagonal of the rhombus
The diagonals of a rhombus bisect each other
∴ `("d"_1/2)^2 + ("d"_2/2)^2` = side2
`8^2 + ("d"_2/2)^2` = 100
⇒ `("d"_2/2)^2` = 100 - 64 = (6)2
⇒ `("d"_2)/(2^2)` = 6
⇒ d2 = 12
Thus, the other diagonal of the rhombus is of length 12cm.
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