Question

Construct a rectangle whose diagonals are of length $8.4cm$ and have an acute angle of ${30}^{\circ }$ between them.

The length of the rectangle is _____ $cm$.

• A. $8.1$
• B. $9.2$
• C. $6.4$
• D. $5.6$

Answer 1

The correct option is A $8.1$

$\Rightarrow$ Draw a line segment $AC=8.4cm$

$\Rightarrow$ Draw a perpendicular line at mid-point of $AC$.

$\Rightarrow$ Construct an angle of ${30}^{\circ }$ with respect to point $A$ and with respect to point $C$.

$\Rightarrow$ Take $O$ as a center cut off $OD=4.2cm$ and $OB=4.2cm$

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

$\Rightarrow$ Thus, $ABCD$ is required rectangle.

$\Rightarrow$ We have to measure length of rectangle.

$\therefore$ $l\left(AB\right)=l\left(CD\right)=8.1cm$