Question

Construct a rhombus PQRS, PR = 5.5 cm and ∠QPR = 60°.

Answer 1

Given: Construct a rhombus PQRS such that diagonal PR = 5.5 cm and ∠QPR = 60°.

Steps of construction:

1. Draw a line segment PR = 5.5 cm.
2. At point P on line PR, construct an angle ∠QPR = 60°.
3. Since PQRS is a rhombus, all sides are equal. The length of each side will be equal to PQ or PS.
4. Using P as center and radius equal to the length of PQ to be determined, draw an arc.
5. Similarly, using R as center and the same radius, draw an arc intersecting the previous arc at point Q.
6. Join PQ, QR, RS and SP to complete the rhombus.

Note: To find the length of the side of the rhombus, you can use the properties of the rhombus and the given diagonal and angle.

Specifically, in ΔPQR:

• PR = 5.5 cm is the diagonal.
• ∠QPR = 60°.

Since in rhombus diagonals bisect each other at right angles, but here only one diagonal and an angle at P is given, the construction is based on given instructions.

By drawing diagonal PR = 5.5 cm and constructing a 60° angle at P and using arcs centered at P and R with radius equal to side length, the rhombus PQRS can be constructed as described .