In the given diagram, the value of AC is 16
In the diagram, we have parallelogram ABCD
From one of the properties of a parallelogram,
"Diagonals of a parallelogram bisect each other"
In the diagram, we can observe that the diagonals bisect at E.
Consider diagonal AC,
Then we can write that
AE = CE
From the question
AE = x² - 8 and CE =2x
Since AE = CE
∴ x² - 8 =2x
Now, we will rearrange the equation and solve for x
The equation becomes
x² -2x - 8 = 0
- Solving the quadratic equation, we get
x² -4x +2x - 8 = 0
x(x -4) +2(x -4) = 0
Then,
(x+2)(x -4) = 0
x + 2 = 0 or x - 4 = 0
x = -2 or x = 4
Since x cannot be less than 0
∴ x = 4
Now,
To determine the value of AC.
In the diagram, we can observe that
AC = AE + CE
Then, we can write that
AC = x² - 8 + 2x
∴ AC = x² +2x - 8
Now, put the value x = 4 into the equation
We get,
AC = 4² +2(4) -8
AC = 16 + 8 -8
∴ AC = 16
Hence, in the given diagram, the value of AC is 16
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