Question

given □ abcd, ac = 28, and ae = 3x - 7, find the value of x.

Explanation:

Step1: Recall the property of parallelogram diagonals

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

Step2: Substitute the given values

Since \(AC = 28\), then \(AE=\frac{28}{2}=14\). And we know \(AE = 3x-7\). So we set up the equation \(3x - 7=14\).

Step3: Solve the equation for \(x\)

Add \(7\) to both sides of the equation: \(3x-7 + 7=14 + 7\), which simplifies to \(3x=21\). Then divide both sides by \(3\): \(x=\frac{21}{3}\).

Answer:

B. 7