Question

parallelogram abcd is a rectangle.
ac = 6y - 1
bd = 4y + 13
what is the value of y?
enter your answer in the box.
y = \boxed{}

Explanation:

Step1: Recall rectangle diagonals property

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

Step2: Set up equation

Substitute \( AC = 6y - 1 \) and \( BD = 4y + 13 \) into \( AC = BD \):
\( 6y - 1 = 4y + 13 \)

Step3: Solve for y

Subtract \( 4y \) from both sides: \( 6y - 4y - 1 = 13 \) → \( 2y - 1 = 13 \).
Add 1 to both sides: \( 2y = 13 + 1 \) → \( 2y = 14 \).
Divide by 2: \( y = \frac{14}{2} = 7 \).

Answer:

\( y = 7 \)