In parallelogram ABCD , AE = x² - 8 and CE = 2x. What is AC?

Solution:

We know that diagonals of parallelograms bisect each other.

Hence, AE = CE

x² - 8 = 2x

x² - 2x - 8 = 0

x² - 2x + 1 - 8 - 1 = 0

x² - 2x + 1 = 9

(x - 1)² = 9

(x - 1) = ± 3

x - 1 = 3 ⇒ x = 4

x - 1 = -3 ⇒ x = -2 .

This is not possible as representing length becomes negative.

Therefore, the required length is 4 units.

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In parallelogram ABCD , AE = x² - 8 and CE = 2x. What is AC?

Summary:

In the given parallelogram ABCD, where AE = x² - 8 and CE = 2x, the value of AC is 4.