Question

In parallelogram ABCD, AE=x^2-6 and CE=5x what is the value of x ? What is AC?

Answer 1

To find the value of x in parallelogram ABCD, set up an equation using the given information and solve for x. Use the fact that the diagonals of a parallelogram bisect each other to find AC.

Step-by-step explanation:

To find the value of x in parallelogram ABCD, we can set up an equation using the given information:

AE = x2-6

CE = 5x

By solving this equation, we can find the value of x.

To find the value of AC, we can use the fact that in a parallelogram, the diagonals bisect each other. So, AC = CD/2. By substituting the value of CD from the earlier equation, we can find AC.

Answer 2

see explanation

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, hence

AE = EC, that is

x² - 6 = 5x ( subtract 5x from both sides )

x² - 5x - 6 = 0 ← in standard form

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 5

However x > 0 ⇒ x = 6

AC = x² - 6 + 5x = 6² - 6 + 5(6) = 36 - 6 + 30 = 60