# Draw the following.Q2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.

Let ABCD be the rhombus such that:

AC = 6.4 cm  (longer diagonal) and BD = 5.2 cm (shorter diagonal)

We know that the diagonals of a rhombus bisect (cut in half) each other perpendicularly, i.e at 60°

In other words, the midpoint of the diagonals coincide.

Steps of construction:

Step 1. Draw a line segment AC =6.4 cm. Now, construct the perpendicular bisector of AC. Let it intersect AC at O.

(Therefore, O is the midpoint of both the diagonals AC and BD)

Step 2. With O as center and radius half of BD = $\frac{5.2}{2} = 2.6\ cm$ , draw two arcs on both sides of AC intersecting the perpendicular bisector at B and D.

Step 3. Join B to A and C. Also join D to A and C.

ABCD is the required rhombus.

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