Question

In parallelogram ABCD, AE = x^2 − 8 and CE = 2x.

What is AC ?

a) 4
b) 8
c) 16
d) 24

Answer 1

i think your answer would be 16 :)

Answer 2

The diagonals of a parallelogram bisect each other, then AE=CE. Since
`AE = x^2-8` and
`CE = 2x`, you have that


`x^2-8=2x`.
Solve this equation:

`x^2-2x-8=0, \\ D=(-2)^2-4\cdot (-8)=4+32=36, \\ √(D)=6, \\ x_(1,2)=(2\pm 6)/(2) =-2,4`.
If x=-2, then CE=-4 that is impossible? because CE is distance and should be positive.
If x=4, then CE=8 and AE=8. The whole diagonal AC=AE+CE=8+8=16.