Question

In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB > BC)

• A. 6 cm from point A
• B. 3 cm from point A
• C. 1.5 cm from point A
• D. Data Insufficient

Answer 1

The correct option is B 3 cm from point A

Given: In parallelogram ABCD, BC = 3 cm.
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.
If we try to construct a rhombus with its each side equal to the longer side of the parallelogram, it will lie outside the parallelogram.
$\Rightarrow$ We have to construct a rhombus with its side length equal to the length of the smaller side which is equal to 3 cm.
$\therefore$ The point E should be 3 cm away from point A
Now, a line EF parallel to AD is drawn from point E and thus we will get the rhombus AEFD.