The problem states that $ABCD$ is a rectangle, where:

• $AB = 2x + 14$ (length),
• $CD = 4x - 12$ (width).

In a rectangle, opposite sides are equal in length. Thus:

$AB = CD$

Step 1: Set the two expressions equal

$2x + 14 = 4x - 12$

Step 2: Solve for $x$

1. Subtract $2x$ from both sides: $14 = 2x - 12$

2. Add $12$ to both sides: $26 = 2x$

3. Divide by $2$: $x = 13$

Step 3: Calculate $AB$ and $CD$

Substitute $x = 13$ into the expressions:

1. $AB = 2x + 14 = 2(13) + 14 = 26 + 14 = 40$,
2. $CD = 4x - 12 = 4(13) - 12 = 52 - 12 = 40$.

Thus, the length of $AB$ and $CD$ is $40$, verifying that the sides are equal as expected.

Let me know if you need further clarifications or additional help!

Here are five related questions:

1. What is the perimeter of the rectangle?
2. How do we find the area of this rectangle?
3. If one diagonal of the rectangle is drawn, what is its length?
4. How do you confirm a figure is a rectangle using only algebra?
5. If $x = 13$, what would be the dimensions of $AD$ and $BC$?

Tip: Always double-check your equations to ensure no sign errors!