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, the diagonals are equal and bisect each other. So \(AC = 2DO\).

Step2: Substitute the given values into the equation

Given \(AC = 48\) and \(DO=7x + 3\), then \(48=2(7x + 3)\).

Step3: Solve the equation for \(x\)

First, expand the right - hand side: \(48 = 14x+6\).
Then, subtract 6 from both sides: \(48 - 6=14x\), so \(42 = 14x\).
Finally, divide both sides by 14: \(x=\frac{42}{14}=3\).

Answer:

\(x = 3\)