Question

In □DEFG, l(EF) = 3.5 cm, l(DE) = 5.5 cm, l(DF) = 7.5 cm, l(DG) = 5 cm, l(EG) = 8 cm.

Answer 1

Given: l(DE)=5.5 cm, l(DF)=7.5 cm, l(DG)= 5cm, l(EF)=3.5 cm and l(EG)=8 cm
First, we draw a rough sketch of quadrilateral DEFG and indicate the given lengths, as shown below.

Steps of Construction:
I. Draw DE = 5.5 cm (the side opposite to the unknown side).


II. Then, draw an arc taking D as centre and GD (5 cm) as radius.

III. Then, draw another arc taking E as centre and EG (7.5 cm) as radius to intersect the previously drawn arc at a point G.

IV. Then, draw an arc taking D as centre and DF (9 cm) as radius on the same side of DE in which point F lies.

V. Then, draw another arc taking E as centre and EF (3.5 cm) as radius to intersect the arc drawn in step IV at point F.

VI. Then, join DG, GE, EF, DF, and DE.

Thus, DEFG is the required quadrilateral.