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

What is AC ?

2 Answers

4 votes

Answer:

96

Explanation:

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User Nick Daria
by
5.3k points
7 votes

Answer:

AC=96 units.

Explanation:

We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.


AE=x^2-16. , and CE=6x .

Note: The diagonals of a parallelogram intersects at mid-point.

Therefore, AE = EC.

Plugging expressions for AE and EC, we get


x^2-16=6x.

Subtracting 6x from both sides, we get


x^2-16-6x=6x-6x


x^2-6x-16=0

Factoriong quadratic by product sum rule.

We need to find the factors of -16 that add upto -6.

-16 has factors -8 and +2 that add upto -6.

Therefore, factor of
x^2-6x-16=0 quadratic is (x-8)(x+2)=0

Setting each factor equal to 0 and solve for x.

x-8=0 => x=8

x+2=0 => x=-2.

We can't take x=-2 as it's a negative number.

Therefore, plugging x=8 in EC =6x, we get

EC = 6(8) = 48.

AC = AE + EC = 48+48 =96 units.


User Fickludd
by
4.8k points
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