Question

Construct a rectangle having diagonal of $7cm$ and length of one of its side is $4cm$. Find its area also

Answer 1

$Diagonal=7cm$ and length of one side $=4cm$.
Steps for construction
Step $1$ : Draw a rough diagram and mark the given measurements.
Step $2$ : Draw a line segment $AB=4cm$.
Step $3$ : Construct $\overrightarrow{BX}\perp \overrightarrow{AB}$.
Step $4$ : With $A$ as centre, draw an arc of radius $7cm$ which cuts $\overrightarrow{BX}$ at $C$.
Step $5$ : With $BC$ as radius draw an arc above $\overline{AB}$ with $A$ as centre.
Step $6$ : With C as centre, and $4cm$ as radiusdraw an arc to cut the previous arc at $D$.
Step $7$ : Join $\overline{AD}$ and $\overline{CD}.ABCD$ is the required rectangle.
Step $8$ : Measure the length of $BC.BC=l=5.8cm$