In trapezoid abcd with bases ab and dc , diagonals intersect at point o. find the length of diagonal bd , if bo=6 cm and: ao/oc = 3/1

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

it is given that

and BO=6 cm

so we can write

cross multiply

divide both side by 3

OD= 2 cm

now we have

BD = BO +OC

BD = 6 cm + 2 cm

BD= 8 cm