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Answer:
To find the length of each diagonal of the rectangle ABCD, you can use the property that in a rectangle, the diagonals are equal in length. This means that:
\[
AC = BD
\]
Given:
- \( AC = y + c \)
- \( BD = 3y - 4 \)
Since the diagonals are equal:
\[
y + c = 3y - 4
\]
Now, solve for \( y \):
1. Subtract \( y \) from both sides:
\[
c = 2y - 4
\]
2. Add 4 to both sides:
\[
c + 4 = 2y
\]
3. Divide by 2:
\[
y = \frac{c + 4}{2}
\]
Now that you have \( y \), you can substitute it back into the expression for \( AC \) or \( BD \) to find the length of the diagonal.
Using \( AC = y + c \):
\[
AC = \frac{c + 4}{2} + c
\]
Simplifying:
\[
AC = \frac{c + 4 + 2c}{2} = \frac{3c + 4}{2}
\]
So, the length of each diagonal is \( \frac{3c + 4}{2} \).