Question

Construct a quadrilateral $ABCD$, when $AB=6.3cm,BC=CD=4.2cm$ and $\angle ABC=\angle BCD={90}^{\circ }.$
Find the length of side $AD$ and $m\angle BAD$.

• A. $AD=3.5$ $cm$, ${70}^{\circ }$
• B. $AD=4.7$ $cm$, ${65}^{\circ }$
• C. $AD=4.5$ $cm$, ${70}^{\circ }$
• D. $AD=3.5$ $cm$, ${65}^{\circ }$

Answer 1

The correct option is B $AD=4.7$ $cm$, ${65}^{\circ }$

Step 1: Draw base $BC$ of length $4.2cm$.

Step 2: Draw lines of at an angle of ${90}^{\circ }$ from points $B$ and $C$.

Step 3: Make an arc of radius $6.3cm$ on the perpendicular line from $B$ and mark the point as $A$.

Step 4: Make an arc of radius $4.2cm$ on the perpendicular line from $C$ and mark the point as $D$.

Step 5: Join $A-D$

$\square ABCD$ is the required quadrilateral.

Upon measuring $AD$, we get the length as $4.7cm$ approx. and $m\angle BAD={65}^{\circ }$