Question

Find the length of each side of a rhombus whose diagonals are 24cm and 10cm long. 

Answer 1

 

Suppose ABCD is a rhombus.
We know that the diagonals of a rhombus perpendicularly bisect each other. 

∴ ∠𝐴𝑂𝐵 = `90^0` , 𝐴𝑂 = 12 𝑐𝑚 𝑎𝑛𝑑 𝐵𝑂 = 5 𝑐𝑚
Now, In right triangle AOB
By using Pythagoras theorem we have 

 `AB^2=AO^2+BO^2` 

`=12^2+5^2` 

`=144+25` 

`=169` 

∴` AB^2=169` 

⇒ AB=13 cm 

Since, all the sides of a rhombus are equal.
Hence, AB = BC = CD = DA = 13 cm