Question
Construct a rectangle whose one side is $3\ cm$ and a diagonal equal to $5\ cm$.
✓
Answer
Diagonals of a rectangle $\&$ opposite sides are equal. All the angles of rectangle are right angle.
So, $\text{AC} = 5\ cm$
$\text{AB} = 3\ cm$
Steps of Construction:
$1.$ Draw $\text{AB} = 3\ cm$
$2.$ Draw a ray $\text{BX}$ such that $\angle\text{ABX}=90^\circ$
$3.$ Mark a point $D$ such that $\text{AC} = 5\ cm$
$4.$ With $B$ as centre, draw an arc of radius $5\ cm$. With $C$ as centre, draw an another arc of radius $3\ cm$ which intersect first arc at a point, suppose $D$.
$5.$ Join $\text{CD}$ and $\text{AD}$.
Hence, $\text{ABCD}$ is the required rectangle.
So, $\text{AC} = 5\ cm$
$\text{AB} = 3\ cm$
Steps of Construction:
$1.$ Draw $\text{AB} = 3\ cm$
$2.$ Draw a ray $\text{BX}$ such that $\angle\text{ABX}=90^\circ$
$3.$ Mark a point $D$ such that $\text{AC} = 5\ cm$
$4.$ With $B$ as centre, draw an arc of radius $5\ cm$. With $C$ as centre, draw an another arc of radius $3\ cm$ which intersect first arc at a point, suppose $D$.
$5.$ Join $\text{CD}$ and $\text{AD}$.
Hence, $\text{ABCD}$ is the required rectangle.
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