Question

Construct a rectangle whose diagonal = 5.8 cm and angle between the diagonals is ${50}^{\circ }$.

Answer 1

$\Rightarrow$ Draw line segment $BD=5.8cm$

$\Rightarrow$ Draw a perpendicular bisector $PQ$ of the line segment $BD$ intersecting $BD$ at point $O.$

$\Rightarrow$ Draw a line $XY$ passing through point $O$ making an angle ${50}^o$ with $BD$.

$\Rightarrow$ Diagonals of a rectangle bisect each other.

$\Rightarrow$ Hence, take $O$ as the center and radius$=2.9$, cut two arcs on both sides of point $O$ cutting line $XY$ at points $A$ and $C.$

$\Rightarrow$ Join $AB,CD,BC$ and $AD$.

$\Rightarrow$ $ABCD$ is the required rectangle.