Question

If $ABCD$ is a rectangle and $AC=12$ inch then find $OA$ and $BD$.

• A. $BD=12$ inch and $OA=6$ inch
• B. $BD=10$ inch and $OA=6$ inch
• C. $BD=10$ inch and $OA=5$ inch
• D. None of the above

Answer 1

The correct option is A $BD=12$ inch and $OA=6$ inch

Given: $ABCD$ is a rectangle and $AC=12$ inch

Now, as per the given figure,
$AC$ and $BD$ are diagonals and as we know diagonals of a rectangle are of equal lengths.
$\therefore AC=BD=12\text{inch}$

Diagonals of rectangles are bisected at their point of intersection
$\therefore OA=\frac{AC}{2}=\frac{12}{2}=\frac{6\times 2}{2}=6\text{inch}$

Therefore, $BD=12\text{inch}$ and $OA=6\text{inch}$
(a) is the correct option.