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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)

  1. 6 cm from point A
  2. 3 cm from point A
  3. 1.5 cm from point A
  4. Data Insufficient


Solution

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.
We have to construct a rhombus with its side length equal to the length of the smaller side which is equal to 3 cm.
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.

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