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Class 8-9-10, JEE & NEET
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Find the length of each side of a rhombus whose diagonals are 24 cm and 10 cm long.
Suppose ABCD is a rhombus.
We know that the digonals of a rhombus perpendicularly bisect each other.
∴ ∠AOB = 90, AO = 12 cm and BO = 5 cm
Now, In right triangle AOB
By using Pythagoras theorem we have
AB = AO + BO
= 12 + 5
= 144 + 25
∴AB = 169
⇒ AB = 13 cm
Since, all the sides of a rhombus are equal.
Hence, AB = BC = CD = DA = 13 cm