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.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. (Considering ‘
l’ 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 and
A2A3 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.