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