Question

lines \\(overline{ac}\\) and \\(overline{bd}\\) are diagonals of abcd. what value of x makes abcd a rectangle if ac = x + 29 and bd = 4x - 1. (1 point) x = 6 x = 10 x = 12 x = 15

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal. So, \(AC = BD\).

Step2: Set up the equation

Given \(AC=x + 29\) and \(BD = 4x-1\), we have the equation \(x + 29=4x-1\).

Step3: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(29=3x - 1\).
Add \(1\) to both sides: \(30 = 3x\).
Divide both sides by \(3\): \(x=\frac{30}{3}=10\).

Answer:

\(x = 10\)