Question

parallelogram abcd is a rectangle
cx = 3y - 4
bd = 2y
what is the value of y?
enter your answer in the box.
y = \boxed{}
(image: rectangle abcd with diagonals intersecting at x)

Explanation:

Step1: Recall rectangle diagonal property

In a rectangle, diagonals are equal and bisect each other. So \( BD = AC \) and \( CX=\frac{1}{2}AC \), which implies \( BD = 2CX \).

Step2: Substitute given expressions

Given \( CX = 3y - 4 \) and \( BD = 2y \), from \( BD = 2CX \), we get \( 2y=2(3y - 4) \).

Step3: Solve the equation

Expand the right - hand side: \( 2y = 6y-8 \).
Subtract \( 2y \) from both sides: \( 0 = 6y - 2y-8 \), i.e., \( 0 = 4y-8 \).
Add 8 to both sides: \( 4y=8 \).
Divide both sides by 4: \( y = 2 \).

Answer:

\( y = 2 \)