Question

# How can we construct a rhombus inside a parallelogram in which the smaller side is two-third the larger side?

A
Find the point which divides the larger side in the ratio of 2:3 and then draw a line parallel to smaller side.
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
Measure with a scale and identify the point on the larger side and construct a rhombus.
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
Using the length of the longer side construct a rhombus by extending the smaller side.
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
Find the point which divides the larger side in the ratio of 2:1 and then draw a line parallel to smaller side.
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## 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 (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.

Suggest Corrections
0
Join BYJU'S Learning Program
Select...
Related Videos
Constructing Similar Triangles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
Select...