Question

The lengths of the diagonals of a rhombus are $24cm$ and $10cm$. Find each side of the rhombus.

Answer 1

The diagonals of a rhombus bisect each other perpendicularly.

Hence $CO=OA=12cm$

$DO=OB=5cm$

Consider $△DOC$, $\angle DOC={90}^{\circ }$

Applying Pythagoras theorem

$(DO{)}^2+(OC{)}^2=(DC{)}^2$

$(5{)}^2+(12{)}^2=(DC{)}^2$

$25+144=(DC{)}^2$

$(DC{)}^2=169$

$DC=\sqrt{169}=13$

Length of each side of rombus $=13cm$