Question

Diagonals AC and BD of a parallelogram ABCD intersect each other at O if OA=3cm and OD=2cm determine the length of AC and BD

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{In parallelogram ABCD, }$

$\textsf{Diagonals AC and BD intersect at O and OA=3 cm, OD=2 cm}$

$\underline{\textsf{To find:}}$

$\textsf{Length of AC and BD}$

$\underline{\textsf{Solution:}}$

$\textsf{We know that,}$

$\textsf{"Diagonals of  parallelogram bisect each other"}$

$\implies\mathsf{OA=OC}\,\textsf{and}\,\mathsf{OB=OD}$

$\implies\textsf{OC=3 cm and OB= 2 cm}$

$\textsf{Now}$

$\mathsf{AC=OA+OC=3+3=6}\,\textsf{cm}$

$\mathsf{BD=OB+OD=2+2=4}\,\textsf{cm}$

$\underline{\textsf{Answer:}}$

$\textsf{Length of AC is 6 cm and}$

$\textsf{Length of BD is 4 cm}$

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Answer 2

Step-by-step explanation:

Here, ABCD is a parallelogram and AC and BD are diagonals of parallelogram intersect each other at O.

OA=3cm and OD=2cm

We know that, diagonals of a parallelogram bisect each other.

∴ AO=OC and BO=OD

⇒ AC=2×OA=2×3cm=6cm

⇒ BD=2×OD=2×2cm=4cm

∴ The length of the diagonals AC and BD are 6cm and 4cm