Question

The lengths of the diagonals PR and QS of a rhombus are $20$ $cm$ and $48$ $cm$ respectively, find the length of each side of the rhombus.

Answer 1

Here, $PQRS$ is a rhombus.

$PR=20,cm$ and $QS=48cm$

We know the diagonals of a rhombus bisect each other perpendicularly.

$\therefore$ $PR\perp QS$

$PO=\frac{1}{2}\times PR=\frac{1}{2}\times 20cm=10cm$

$OS=\frac{1}{2}\times QS=\frac{1}{2}\times 48cm=24cm$

$△POS$ is a right-angled triangle.

$\therefore$ $(PS{)}^2=(PO{)}^2+(OS{)}^2$ [ By Pythagoras theorem ]

$\Rightarrow$ $(PS{)}^2=(10{)}^2+(24{)}^2$

$\Rightarrow$ $(PS{)}^2=100+576$

$\Rightarrow$ $(PS{)}^2=676$

$\Rightarrow$ $PS=26cm$

All sides of a rhombus are equal.

$\therefore$ $PQ=QR=RS=SP=26cm$