Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, determine the lengths of AC and BD.

Solution:

Given

ABCD is a parallelogram with AC and BD as the diagonals intersecting at O

OA = 3 cm

OD = 2 cm

As the diagonals of a parallelogram bisect each other

AO = OC

BO = OD

AC = 2 × OA = 2 × 3 = 6 cm

BD = 2 × OD = 2 × 2 = 4 cm

Therefore, the lengths of AC and BD are 6 cm and 4 cm.

✦ Try This: Diagonals PR and QS of a parallelogram PQRS intersect each other at O. If OP = 4 cm and OS = 3 cm, determine the lengths of PR and QS.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8

NCERT Exemplar Class 9 Maths Exercise 8.2 Problem 1

Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, determine the lengths of AC and BD

Summary:

Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, the lengths of AC and BD are 6 cm and 4 cm respectively

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