Question

In the given figure, $ABCD$ is a parallelogram, diagonals $BD$ and $AC$ intersect each other at $E$. If $BE+CE=8$ cm, then $AC+BD$ is equal to

• A. $16$ cm
• B. $14$ cm
• C. $20$ cm
• D. $24$ cm

Answer 1

The correct option is A $16$ cm

Given: $ABCD$ is a parallelogram
We know that the diagonals of a parallelogram bisect each other.
$\Rightarrow$ The diagonals $BD$ and $AC$ bisect each other.

$\therefore AE=EC$ and $BE=ED$

We know, $AC+BD=AE+EC+BE+ED$

$=EC+EC+BE+BE$

$=2\times (EC+BE)$

$=$ $2\times 8$ cm

$=16$ cm