Question

If $ABCD$ is a parallelogram such that $AC=10$ inch and $BD=8$ inch then the lengths of $OA$ and $OB$ will be and respectively.

• A. $3$ inch
• B. $4$ inch
• C. $5$ inch
• D. $6$ inch

Answer 1

Answer: (B), (C)

$5$ inch


Given: $ABCD$ is a parallelogram
$AC=10$ inch and $BD=8$ inch

Now, as per the figure, $AC$ and $BD$ are diagonals of parallelogram $ABCD$ which intersets at point $O$.

As we know, diagonals of parallelogram are bisected at their point of intersection. Therefore, diagonals $AC$ and $BD$ will be bisected at point $O$.
$⟹OA=OC=\frac{AC}{2}$

$⟹OA=\frac{10}{2}=\frac{5\times 2}{2}=5$ inch

Similarly, $OB=OD=\frac{BD}{2}$

$⟹OB=\frac{8}{2}=\frac{4\times 2}{2}=4$ inch

Therefore, $OA=5$ inch and
$OB=4$ inch