Answer: BD = 108
Step-by-step explanation:
In a parallelogram, the opposite sides are congruent and the diagonals bisect each other. It means that they bisect at a midpoint that divides them equally.
Therefore,
AB = DC
AD = BC
BD = AC
Also BE = ED. This means that
7x - 2 = x^2 - 10
x^2 - 10 +2 - 7x = 0
x^2 - 7x -8 = 0
Solving the quadratic equation with factorization method,
x^2 + x - 8x -8 = 0
x(x + 1) -8(x + 1) = 0
x - 8 = 0 or x + 1 = 0
x = 8 or x = -1
Since x cannot be negative,
x = 8
BE = 7×8 - 2 = 54
ED = 8^2 - 10 = 54
BD = BE + ED = 54 +54 = 108
