Question

the length of the diagonals of a rhombus are 16cm and 12cm respectively. find the length of each of its sids​

Answer 1

$\huge{\mathfrak{\magenta{Solution}}$

Let ABCD be the rhombus and AC and BD bisect at point O. AC = 16cm and BD = 12cm.

 

➻ We know that the diagonals of rhombus bisect at right angles.

 ➻  AO=  $\frac{16}{2}$=8

 ➻  BO=$\frac{12}{2}$=8

 ➻  In right angled △AOB,

By using Pythagoras theorem,

 ➻ $\huge{\mathtt{AB^{2} =AO^{2} +BO^{2}}}$

 ➻ $\huge{\mathtt{AB^{2} =8^{2} =6^{2}}$

 ➻ $\huge{\mathtt{AB^{2} =64+36}}$

 ➻ $\huge{\mathtt{AB^{2}=\sqrt{100}}$

 ➻ $\huge{\mathtt{AB=100}$

​  

∴  Side of a rhombus is 10cm.

More Formulae-

Perimeter of Rhombus = 4a (Where a is the side.)

Area of rhombus = ah  (where   a is the length of the side  &h is the height).