Question
Construct a quadrilateral $ABCD$ in which $AB = 4\ cm, AC = 5\ cm, AD = 5.5\ cm$ and $\angle\text{ABC}=\angle\text{ACD}=90^\circ.$
✓
Answer
Steps of construction:
Step 1: Draw $AB = 4\ cm.$
Step 2: Make $\angle\text{B}=90^\circ.$
Step 3:
$AC^2 = AB^2 + BC^2$
$5^2 = 4^2 + BC^2$
$25 - 16 = BC^2$
$BC = 3\ cm$
With $B$ as the centre, draw an arc equal to $3\ cm.$
Step 4: Make $\angle\text{C}=90^\circ.$
Step 5: With $A$ as the centre and radius equal to $5.5\ cm,$ draw an arc and name that point as $D.$
Then, $ABCD$ is the required quadrilateral.
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