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Question
Find the length of each side of a rhombus are 40 cm and 42 cm. find the length of each side of the rhombus.
Solution
Suppose ABCD is a rhombus.
We know that the diagonals of a rhombus perpendicularly bisect each other.
∴ ∠๐ด๐๐ต = 90°, ๐ด๐ = 20 ๐๐ ๐๐๐ ๐ต๐ = 21 ๐๐
Now, In right triangle AOB
By using Pythagoras theorem we have
`AB^2=AQ^2+OB^2`
=`20^2+21^2`
=`400+441`
=`841`
∴ `AB^2=841`
⇒ `AB=29 cm`
Since, all the sides of a rhombus are equal.
Hence, AB = BC = CD = DA = 29 cm
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