Calculate Rectangle Area: Finding Area When Length is 13X and Width is 2X

The problem requires finding the area of rectangle $ABCD$ with side lengths $AD = 2X$ and $DC = 13X$. We will use the formula for the area of a rectangle:

$A = \text{length} \times \text{width}$

Here, the length and width of the rectangle are $AD$ and $DC$. Therefore:

$A = AD \times DC = (2X) \times (13X)$

Step-by-step calculation:

• Multiply the coefficients: $2 \times 13 = 26$.
• Combine the variable terms: $X \times X = X^2$.

Thus, the area of the rectangle is:

$A = 26X^2$

The solution to the problem is $26X^2$, which corresponds to choice 1.