Question

Construct a rhombus PQRS, PR = 5 cm and QS = 8 cm.

Answer 1

Given: Construct a rhombus PQRS with diagonals PR = 5 cm and QS = 8 cm.

Steps of construction:

1. Draw the diagonal QS = 8 cm.

2. Mark the midpoint of QS as O since diagonals of a rhombus bisect each other.

3. Draw the perpendicular bisector of QS at O.

4. From O on the perpendicular bisector, mark points P and R such that PO = OR = half of PR = 2.5 cm since PR = 5 cm.

5. Join points P to Q, P to S, R to Q and R to S.

PQRS is the required rhombus with diagonals PR = 5 cm and QS = 8 cm.

This construction uses the fact that diagonals of a rhombus bisect each other at right angles, so PR and QS intersect at point O, bisecting each other.

Hence, by drawing QS, constructing its perpendicular bisector and setting P and R at distances 2.5 cm from O on the bisector and then joining as above, we obtain the rhombus PQRS.