Question

Parallelogram with adjacent sides 7 centimetres and 4 centimetres; one diagonal 8 centimetres.

Answer 1

Let ABCD be the required parallelogram.

Given: DC = AB = 7 cm

AD = BC = 4 cm

AC = 8 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 7 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 8 cm as the radius, draw an arc which intersects the previously drawn arc at point A.

(4) Join AD and AC.

(5) Taking A as the centre and 7 cm as the radius, draw an arc on the right side of point A.

(6) Taking C as the centre and 4 cm as the radius, draw an arc which intersects the previously drawn arc at point B.

(7) Join AB and BC.

ABCD is the required parallelogram.