Question

The diagonals of rhombus measure $16cm$ and $30cm$. Find its perimeter.

Answer 1

$AC$ and $BD$ are diagonals of a rhombus.

$AC=16,BD=30$

We know that diagonals of rhombus are perpendicular bisectors of each other.

$\therefore$ $AO=8$ and $BO=15$

In right angled $△AOB$

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

$\Rightarrow$ $(AB{)}^2=(8{)}^2+(15{)}^2$

$\Rightarrow$ $(AB{)}^2=64+225$

$\Rightarrow$ $(AB{)}^2=289$

$\Rightarrow$ $AB=17cm$

We know that, all four sides of rhombus are equal.

$\therefore$ Perimeter of rhombus $ABCD=4\times AB$

$=4\times 17$

$=68cm$