Question

question 6 of 10 given ▱abcd, ac = 22, and ae = 2x - 5, find the value of x.
a. 6
b. 13
c. 8
d. 11

Explanation:

Step1: Recall property of parallelogram

In parallelogram \(ABCD\), the diagonals bisect each other. So \(AE=\frac{1}{2}AC\).

Step2: Substitute given values

Since \(AC = 22\) and \(AE=2x - 5\), we have \(2x-5=\frac{1}{2}\times22\).

Step3: Simplify the right - hand side

\(\frac{1}{2}\times22 = 11\), so the equation becomes \(2x-5 = 11\).

Step4: Solve for \(x\)

Add 5 to both sides: \(2x=11 + 5\), \(2x=16\). Then divide both sides by 2: \(x = 8\).

Answer:

C. 8