Question

The diagonals of a rhombus $ABCD$ are $6cm$ and $8cm$. Find the length of a side of the rhombus.

Answer 1

Diagonals of a rhombus bisect each other at right angles.

Let point of intersectio of diagonals be $O$

So, $OD=3cm,OA=4cm$

From Right angled triangle $△AOD$,

$\Rightarrow A{D}^2=O{A}^2+O{D}^2$ (pythoagorus theorem)

$\Rightarrow A{D}^2=4^2+3^2$

$\Rightarrow A{D}^2=16+9$

$\Rightarrow A{D}^2=25$

$\Rightarrow AD=5cm$

$AD$ is side of the rhombus .

So, length of side of the rhombus is $5cm$