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?

• 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

In parallelogram ABCD, given BC = 3 cm.
A line drawn parallel to BC from E divides the parallelogram into two parallelograms. But if a rhombus should be formed, one of the parallelograms should have all sides equal. Since the length of smaller side is fixed, we have to make rhombus with length of sides being equal to length of the smaller side = 3 cm. So the point can lie 3 cm from either point A or point B.