Question

In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, AE=x2−16 , and CE=6x . What is AC ?

The answer is 96.

Answer 1

The answer is 96 when X= 8

Explanation:

We have given that :

AE=
`x^2-16` and CE=
`6x`

where AE and CE are the diagonals of the paralleogram

The diagonals of parallelogram bisect each other therefore,

`x^2-16 = 6x`

⇒
`x^2-6x-16=0`

factors are (x+2)(x-8)=0

setting to each factor 0 the value of x= -2 or x= 8

therefore, two values of AC is

X= -2 ,AC= 2(
`x^2-16`)=2(-12)=-24

X= 8 ,AC= 2(
`x^2-16`)=2(48)=96

The answer is 96 when X= 8