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Question:

Draw a rhombus whose diagonals are 5.2 cm and 6.4 cm long.

Solution:

Steps to draw a rhombus with given diagonals:

  1. Draw the diagonals: Draw a line segment AC of length 6.4 cm. Then draw another line segment BD of length 5.2 cm, such that it bisects AC at point O (the midpoint of AC). Make sure that the diagonals are perpendicular to each other (intersect at a 90-degree angle).

  2. Mark the vertices: The intersection of the diagonals (point O) will be the center of the rhombus. Mark the points where the diagonals intersect the sides of the rhombus as A, B, C, and D. You should have four points forming the vertices of the rhombus.

  3. Join the vertices: Connect the four points A, B, C, and D using a ruler and pencil to form the sides of the rhombus.

Explanation:

A rhombus is a quadrilateral with all sides equal in length. The diagonals of a rhombus bisect each other at a 90-degree angle. Therefore, by constructing the diagonals of the specified lengths, bisecting them, and joining their endpoints, we create a rhombus that satisfies the given conditions. The midpoint of the diagonals serves as the center of symmetry for the rhombus.