Parallelogram ABCD has diagonal segments AC and BD that intersect at E. if BE is ( x + 8) and ED is (5 x), find the length of BD.

BD = 20 units

Step-by-step explanation:

Given that,

Parallelogram ABCD has diagonal segments AC and BD that intersect at E.

BE = (x+8) and ED = 5x

We need to find the length of BD.

BD = BE + ED ...(1)

We know that the diagonals of a parallelogram bisects each other. It means,

BE = ED

x+8 = 5x

8 = 5x - x

8 = 4x

x = 2

BE = (x+8)

= (2+8)

= 10

ED = 5x

= 5(2)

= 10

Put the values in equation (1).

BD = 10 + 10

= 20 units

Hence, the length of BD is 20 units.