Question

quadrilateral pqrs is a rectangle, qt = 15z + 25, and rt = 6z + 34. what is the value of z? z =

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(QT = RT\).

Step2: Set up the equation

Given \(QT = 15z+25\) and \(RT = 6z + 34\), we have the equation \(15z+25=6z + 34\).

Step3: Solve the equation for \(z\)

Subtract \(6z\) from both sides: \(15z - 6z+25=6z-6z + 34\), which simplifies to \(9z+25 = 34\).
Subtract \(25\) from both sides: \(9z+25-25=34 - 25\), so \(9z=9\).
Divide both sides by \(9\): \(z=\frac{9}{9}\).

Answer:

\(z = 1\)