Question

In a parallelogram ABCD its diagonal AC AND BD intersect each other at point O if AC = 12cm and BD= 9cm find : lenghts of OA and OD​

Answer 1

Step-by-step explanation:

Solution:

When diagonal AC and BD intersect each other at point O,

Then OA=OC=\frac{1}{2}ACOA=OC=

2

1

AC

OB=OD=\frac{1}{2}BDOB=OD=

2

1

BD

OA=\frac{1}{2}\times AC=\frac{1}{2}\times12=6\ cmOA=

2

1

×AC=

2

1

×12=6 cm

OB=\frac{1}{2}\times BD=\frac{1}{2}\times9=4.5\ cmOB=

2

1

×BD=

2

1

×9=4.5 cm

Answer 2

Answer:

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.