Question

As shown in the above fig. the diagonals of a rhombus are $20cm$ and $21cm$ respectively, then find the side of rhombus and its perimeter.

Answer 1

REF.Image.

As diagonals of rhombus are perpendicular bisector of each other

$\Rightarrow AO=10,OB=21/2$

Apply Pythagoras theorem $△AOB,$

$A{B}^2={10}^2+\frac{{21}^2}{4}=100+\frac{441}{4}$

$\Rightarrow A{B}^2=\frac{841}{4}\Rightarrow AB=\frac{29}{2}=side$;

Perimeter = $4\times \frac{29}{2}=58$