The correct option is D Find the point which divides the larger side in the ratio of 2:1 and then draw a line parallel to smaller side.
A rhombus is a parallelogram with all sides equal.
To construct a rhombus inside a given parallelogram, we need to use the available lengths of the sides of the parallelogram.
The available sides are l,2l3
’ to be the length of the longer side).
If we try to construct a rhombus with side l
, it will lie outside the parallelogram.
So taking the side 2l3
to be one of the sides of the rhombus, we need to locate points on the longer side such that their length is 2l3
Steps of Construction:
a) Let us start by constructing a ray AX which makes an acute angle with one of the longer sides AB.
b) Now mark A1,A2,A3
on ray AX such that A1A2=A2A3=AA1
. (This is done in order to divide AA2
in the ratio 2:1.)
c) Now join A3B
and draw A2E
parallel to A3B
such that the point E lies on the line segment AB. By Basic Proportionality Theorem, AEEB=AA2A2A3=21
d) Now draw a line from point E parallel to BC. The point where this line intersects CD be F.
e) AEFD is the required rhombus.