Question

Given parallelogram ABCD, diagonals AC and BD intersect at point E.AE = 2x, BE = y + 10, CE = x + 2 and DE = 4y - 8. Find y.

Answer 1

The diagram below show the situation given in the problem:

We know that the diagonals of a parallelogram bisect each other, which means that AE=CE and BE=DE; using the second equality we have that:

$\begin{gathered} y+10=4y-8 \\ 4y-y=10+8 \\ 3y=18 \\ y=\frac{18}{3} \\ y=6 \end{gathered}$

Therefore, the value of y is 6 and the answer is A.