What is the area, in square inches, of a rectangle with a length of 7 inches

Choice C is correct. The area, $A$, of a rectangle is given by the formula $A=\mathcal{l}w$, where $\mathcal{l}$ represents the length of the rectangle and $w$ represents its width. It’s given that the rectangle has a length of $7$ inches and a width of $6$ inches. Substituting $7$ for $\mathcal{l}$ and $6$ for $w$ in the formula $A=\mathcal{l}w$ yields $A=\left(7\right)\left(6\right)$, or $A=42$. Thus, the area, in square inches, of the rectangle is $42$.

Choice A is incorrect. This is the sum, not the product, of the length and width of the rectangle.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is twice the area, in square inches, of the rectangle.