Question

$ABCD$ is rectangle. Its diagonals meet at $O.$ Find $AC,$ if $OA=(3x+5)cm$ and $OB=(2x+9)cm$

Answer 1

Here, $ABCD$ is a rectangle with diagonals $AC$ and $BD.$

We know that the diagonals of rectangles are equal and bisect each other.

$AC=BD$

$\Rightarrow$ $\frac{1}{2}\left(AC\right)=\frac{1}{2}\left(BD\right)$

$\Rightarrow$ $OA=OB$

$\Rightarrow$ $3x+5=2x+9$

$\Rightarrow$ $x=4$

Hence,

$OA=3\times 4+5$

$=17$

Now,

$AC=2\left(OA\right)$

$\Rightarrow AC=2\times 17$
$\Rightarrow AC=34cm$