Question

$ABCD$ is a rectangle. Its diagonals meet at $O$.
Find '$x$', if $OA=2x+4$ and $OD=3x+1$.

• A. $2$
• B. $3$
• C. $-3$
• D. $-2$

Answer 1

The correct option is B $3$

$\Rightarrow$ In the given figure ABCD is a rectangle.

$\Rightarrow$ $OA=2x+4$ and $OD=3x+1$ [Given]

$\Rightarrow$ AC and BD are diagonals of a rectangle.

$\Rightarrow$ We know that diagonals of a rectangle are equal.

$\Rightarrow$ So, AC = BD

We can also write it as,

$\Rightarrow$ $2\times OA=2\times OD$

$\Rightarrow$ $2\times (2x+4)$ $=2\times (3x+1)$

$\Rightarrow$ $2x+4=3x+1$

$\therefore$ $x=3$