Answer:
BD = 8 cm
Step-by-step explanation:
Diagonals of trapezoid divides each other in equal ratio.
if ABCD is a trapezoid and the diagonals AC and BD intersect at point O
then we have
[tex]\frac{AO}{OC} =\frac{OB}{OD}[/tex]
it is given that
[tex]\frac{AO}{OC} =\frac{3}{1}[/tex] and BO=6 cm
so we can write
[tex]\frac{3}{1} =\frac{6}{OD}[/tex]
cross multiply
[tex]3 OD=6[/tex]
divide both side by 3
OD= 2 cm
now we have
BD = BO +OC
BD = 6 cm + 2 cm
BD= 8 cm
