Question

question 10 of 10 given parallelogram abcd, ac = 28, and ae = 3x - 7, find the value of x. a. 7 b. 13 c. 14 d. 6

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 \(AC = 28\) and \(AE=3x - 7\), we have \(3x-7=\frac{28}{2}\).

Step3: Simplify the right - hand side

\(\frac{28}{2}=14\), so the equation becomes \(3x - 7=14\).

Step4: Solve for \(x\)

Add 7 to both sides: \(3x=14 + 7\), \(3x=21\). Then divide both sides by 3: \(x=\frac{21}{3}=7\).

Answer:

A. 7