elogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of BD. A. 6 B. 16 C.

Question

2 years ago

8

18 D. 32

1 answer:

slega [8] · Answer 1 · 2022-09-20T01:34:57+03:00

Answer:

D

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, thus

DE = BE , substitute values

4y - 8 = y + 10 ( subtract y from both sides )

3y - 8 = 10 ( add 8 to both sides )

3y = 18 ( divide both sides by 3 )

y = 6

Thus

BD = y + 10 + 4y - 8 = 5y + 2 = 5(6) + 2 = 30 + 2 = 32 → D