Question

Parallelogram with one side 5 centimetres; diagonals 8 centimetres and 6 centimetres.

Answer 1

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

Given: DC = 5 cm

AC = 6 cm, BD = 8 cm

We know that diagonals of a parallelogram bisect each other.

∴ OC = OA = = 3 cm

OD = OB = = 4 cm

Here is the rough sketch of the required parallelogram.

The steps of construction are as follows:

(1) Draw a line segment DC of length 5 cm.

(2) Taking D as the centre and 4 cm as the radius, draw an arc on the upper side of line segment DC.

(3) Taking C as the centre and 3 cm as the radius, draw an arc intersecting the previously drawn arc at point O.

(4) Join OD and OC.

(5) Now extend DO and CO to form rays DX and CY respectively.

(6) Taking O as the centre and 4 cm as the radius, draw an arc which intersects ray DX at point B.

(7) Taking O as the centre and 3 cm as the radius, draw an arc which intersects ray CY at point A.

(8) Join AD, AB and BC.

ABCD is the required parallelogram.