Question

If the diagonals of a rhombus are 24 cm, 10 cm. Find the length of its side.

Answer 1

Let $ABCD$ be the rhombus where, $AC=10cm$ and $BD=24cm$

Let $AC$ and $BD$ intersect each other at $O.$Now, diagonals of rhombus bisect each other at right angles.

Thus, we have

$AO=\frac{1}{2}\times AC=\frac{1}{2}\times 10=5cm$ and

$BO=\frac{1}{2}\times BD=\frac{1}{2}\times 24=12cm$

In right angled $△AOB,$

$\Rightarrow$ $(AB{)}^2=(AO{)}^2+(BO{)}^2$

$\Rightarrow$ $(AB{)}^2=(5{)}^2+(12{)}^2$

$\Rightarrow$ $(AB{)}^2=25+144$

$\Rightarrow$ $(AB{)}^2=169$

$\therefore$ $AB=13cm$

$\therefore$ The length of each side of rhombus is $13cm.$