Question

ABCD is a parallelogram where AC and BD are the two diagonals. If BD is 6 cm more than AC and AE = 5 cm, find the length of BE.

Answer 1

Given, ABCD is a parallelogram, AC and BD are diagonals, and hence they bisect each other.
Then, AE = EC and BE = ED ----- (i)

Given AE = 5cm = EC (Diagonals bisect each other)
Then AC = AE + EC = 5 + 5 = 10 cm

BD = 6 + AC (Given)
$\Rightarrow$ BD = 6 + 10 = 16 cm

From the figure, BD = BE + ED .

From (i), BD = BE + BE = 2 $\times$ BE
$\Rightarrow$ 16 = 2 $\times$ BE
$\Rightarrow$ BE =$\frac{16}{2}$ = 8

$\therefore$ Length of BE = 8 cm