Question

parallelogram abcd is a rectangle.
ac = 2y + 7
bd = 3y - 4
what is the value of y?
enter your answer in the box.
y =

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal. So, \(AC = BD\).
Given \(AC=2y + 7\) and \(BD = 3y-4\), we set up the equation \(2y+7=3y - 4\).

Step2: Solve the equation for \(y\)

Subtract \(2y\) from both sides of the equation:
\(2y+7-2y=3y - 4-2y\)
\(7=y - 4\).
Then add \(4\) to both sides:
\(7 + 4=y-4 + 4\)
\(y=11\).

Answer:

\(11\)