Question

Construct a parallelogram whose diagonal are $8.4$ cm and $10.6$ cm and an angle between them is ${50}^o$.

Answer 1

$\Rightarrow$ Draw $AC=8.4cm$

$\Rightarrow$ Bisect $AC$ at $O.$

$\Rightarrow$ Make $\angle COX={50}^o$ and produce $XO$ to $Y$.

$\Rightarrow$ Set off $OB=\frac{1}{2}\times 10.6=5.3cm$ and $OD=\frac{1}{2}\times 10.6=5.3cm$ as shown.

$\Rightarrow$ Join $AB,BC,CD$ and $DA$

Then, $ABCD$ is the required parallelogram.