Question

because congruent diagonals prove that a parallelogram is a rectangle, what value of x proves that parallelogram abcd is a rectangle if ac = 48 and do = 7x + 3?

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, diagonals are equal and bisect each other. So \(AC = BD\) and \(DO=\frac{1}{2}BD\). Since \(AC = 48\), then \(BD=48\) and \(DO=\frac{1}{2}\times48 = 24\).

Step2: Solve the equation for \(x\)

Set \(7x + 3=24\). Subtract 3 from both sides: \(7x=24 - 3=21\). Then divide both sides by 7: \(x=\frac{21}{7}=3\).

Answer:

\(x = 3\)