Question

Parallelogram with diagonals 6 centimetres and 7 centimetres; angle between them 70°.

Answer 1

Let ABCD be the required parallelogram with diagonals AC and BD intersecting at point O.

Given: AC = 6 cm, BD = 7 cm

∠DOC = 70°

We know that diagonals of a parallelogram bisect each other.

∴ OC = OA = = 3 cm

OD = OB = = 3.5 cm

Here is the rough sketch of the required parallelogram.

The steps of construction are as follows:

(1) Draw line segment AO of length 3 cm and produce AO to a point C such that OC = OA.

(2) At point O, draw ∠COP of measure 70°.

(3) Taking O as the centre and 3.5 cm as the radius, draw an arc which intersects ray OP at point D.

(4) Produce OD to a point B such that OD = OB.

(5) Join AD, DC, CB and BA.

ABCD is the required parallelogram.