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.

Answer 1

\[\text { Steps of construction: } \]

\[\text { Step I: Draw AB = 6 cm } . \]

\[\text { Step II: With A as the centre and radius 5 . 5 cm, draw an arc } . \]

\[\text { Step III : With B as the centre and radius 6 . 1 cm, draw an arc to intersect the arc drawn in StepII at D  }. \]

\[\text { Step IV: With B as the centre and radius 3 . 7 cm, draw an arc on the side } . \]

\[\text { Step V : With D as the centre and radius 5 . 7 cm, draw an arc to intersect the arc drawn in StepIV at C  }. \]

\[\text { Step VI: Join BD, DA, BC and CD  }. \]

\[\text { The quadrilateral ABCD so obtained is the required quadrilateral } .\]