using ruler and compass only: construct a rhombus ABCD with AB= 6 cm and diagonal AC= 7 cm . Hence measure and write down the length of the diagonal BD
Answers
Given:
A rhombus ABCD with AB= 6 cm and diagonal AC= 7 cm .
To find:
The length of the diagonal BD.
Solution:
Steps of construction:
Draw a line AC with a scale of 7 cm.
Since all the sides of a rhombus are equal and as given AB = 6 cm.
Therefore, we have, AB = BC = CD = DA = 6 cm.
From points A and C draw arcs with a scale of 6 cm, above and below the line AC.
The points where these arcs meet, mark them as B and D.
Join AB, AD and CB, CD.
Hence the required construction of rhombus ABCD.
Join BD, hence the required another diagonal of rhombus ABCD.
The measure of the diagonal BD is 9.7 cm.
Steps of construction:
(i) Construct triangle OBC such that
OB = ½ x BD = ½ x 4.4cm = 2.2cm
OC = ½ x AC = ½ x 8.6cm = 4.3cm
Since, diagonals of || gm bisect each other and BC = 4cm
(ii) Produce BO to D such that BO = OD = 2.2cm
(iii) Produce CO to A such that CO = OA = 4.3cm
(iv) Join AB, AD and CD
Thus, ABCD is the required parallelogram.
(v) Measure the side AB, AB = 5.6cm