Construct a rectangle whose one diagonal has length 5 cm and the angle between the diagonals is 50 degrees.

Given: The length of a diagonal of a rectangle as 5 cm and the angle between the diagonals of the rectangle as 50 degrees.

To find: We have to construct the rectangle according to the given measurements.

Solution:

Steps of Construction:

1. Draw line segment AC = 5 cm

2. Draw a perpendicular bisector PQ of the line segment AC intersecting AC at point O.

3. Draw a line XY passing through point O making an angle 50° with AC.

4. Diagonals of a rectangle bisect each other. Hence, take O as the center and radius = 2.5 cm, cut two arcs on both sides of point O cutting line XY at points B and D.

5. Join AB, CD, BC, and AD.

6. ABCD is the required rectangle

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Updated on: 10-Oct-2022

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