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labwork [276]
3 years ago
5

In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, AE=2x2−3x , and CE=x2+4 .

Mathematics
2 answers:
EastWind [94]3 years ago
8 0

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.

AE=CE

2x^2-3x=x^2+4

2x^2-3x-x^2-4=0

x^2-3x-4=0

x^2-4x+x-4=0

x(x-4)+1(x-4)=0

(x-4)(x+1)=0

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

AC=2CE

AC=2(x^2+4)

Let he value of x=4.

AC=2(4^2+4)

AC=2(20)

AC=40

Therefore the length of AC is 40.

Let he value of x=-1.

AC=2((-1)^2+4)

AC=2(5)

AC=10

Therefore the length of AC is 10.

spin [16.1K]3 years ago
4 0
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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