Question

quadrilateral pqrs is a rectangle, pr = 7y + 80, and qs = 15y. what is the value of y?

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal. So \(PR = QS\).
Given \(PR=7y + 80\) and \(QS = 15y\), we set up the equation \(7y+80=15y\).

Step2: Solve the equation for \(y\)

Subtract \(7y\) from both sides of the equation:
\(7y+80-7y=15y - 7y\)
\(80 = 8y\)
Divide both sides by \(8\):
\(y=\frac{80}{8}\)

Answer:

\(y = 10\)