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. 

The lengths of the diagonals of a rhombus are 40 cm and 42 cm. Find the length of each side of the rhombus.

Answer 1

 

Suppose ABCD is a rhombus.
We know that the diagonals of a rhombus perpendicularly bisect each other.
∴ ∠𝐴𝑂𝐵 = 90°, 𝐴𝑂 = 20 𝑐𝑚 𝑎𝑛𝑑 𝐵𝑂 = 21 𝑐𝑚
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