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)

- 6 cm from point A
- 3 cm from point A
- 1.5 cm from point A
- 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.

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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