Question:
Construct, if possible, a quadrilateral ABCD given AB = 6 cm, BC = 3.7 cm, CD = 5.7 cm, AD = 5.5 cm and BD = 6.1 cm. Give reasons for not being able to construct it, if you cannot.
Solution:
Steps of construction:
Step I: Draw $\mathrm{AB}=6 \mathrm{~cm} .$
Step II : With $\mathrm{A}$ as the centre and radius $5.5 \mathrm{~cm}$, draw an arc.
Step III : With B as the centre and radius $6.1 \mathrm{~cm}$, draw an arc to intersect the arc drawn in StepII at D.
Step IV : With B as the centre and radius $3.7 \mathrm{~cm}$, draw an arc on the side.
Step V : With D as the centre and radius $5.7 \mathrm{~cm}$, draw an arc to intersect the arc drawn in StepIV at C.
Step VI : Join BD, DA, BC and CD.
The quadrilateral ABCD so obtained is the required quadrilateral.
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