Question

given that quadrilateral abcd is a rectangle with ac = 7x and bd = 2x + 5, find the value of x.
(1 point)
x =

Explanation:

Step1: Use the property of rectangle diagonals

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

Step2: Set up the equation

Given \(AC = 7x\) and \(BD=2x + 5\), we have the equation \(7x=2x + 5\).

Step3: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(7x-2x=2x + 5-2x\), which simplifies to \(5x = 5\).
Divide both sides by \(5\): \(x=\frac{5}{5}\).

Answer:

\(x = 1\)