In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, AE=2x2−3x , and CE=x2+4 .
2 answers:
Answer:
The length of AC is either 10 units or 40 units.
Step-by-step explanation:
it is given that parallelogram ABCD and diagonals AC and BD intersect at point E.
According to the property of parallelogram, the diagonals are intersecting each other at their midpoint.







By zero product property, equate each factor equal to 0. So the value of x is 4 and -1.


Let he value of x=4.



Therefore the length of AC is 40.
Let he value of x=-1.



Therefore the length of AC is 10.
If the diagonals of the parallelogram intersect with each other, this means that the diagonals bisect each other. Thus,
AE = CE
Substituting the equations,
2x² - 3x = x² + 4
The values of x from the equation are equal to 4 and -1.
AE = 2(4)² - 3(4) = 20
Hence, AC is equal to 40.
Answer: 40 units
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