Question

a rectangle is 8 feet long. its width is represented by \seven plus x feet\. which expression represents the area, in square feet, of the rectangle? a 15 + x

Explanation:

Step1: Recall the area formula for a rectangle

The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \).

Step2: Identify the length and width

The length of the rectangle is 8 feet. The width is \( (7 + x) \) feet (since it is "seven plus \( x \) feet").

Step3: Substitute into the area formula

Substitute the length and width into the formula: \( A = 8\times(7 + x) \). Using the distributive property (also known as the distributive law of multiplication over addition), \( 8\times(7 + x)=8\times7 + 8\times x = 56+8x \). Wait, but looking at the options (even though some are cut off, let's re - evaluate). Wait, maybe there was a typo in the problem statement or the options. Wait, the length is 8, width is \( 7 + x \), so area is \( 8(7 + x)=56 + 8x \). But if we look at the options provided (A: \( 15 + x \), but maybe the original problem had a different length or width? Wait, maybe the length was 8 and width was \( 7 + x \), but let's check again. Wait, perhaps the user made a typo, but assuming the standard formula:

Wait, maybe the problem was supposed to have length 8 and width \( 7 + x \), so the area is \( 8(7 + x)=56 + 8x \). But if we look at the options, maybe there was a mistake. Alternatively, if the width was \( 7 + x \) and length 8, the area is \( 8(7 + x)=56 + 8x \). But since the options are not fully visible, but based on the formula, the correct expression should be \( 8(7 + x) \) or expanded as \( 56+8x \).

But if we assume that the options are like:

If option D (assuming from the image) is \( 8(7 + x) \) or similar, but based on the formula for the area of a rectangle (length times width), with length 8 and width \( 7 + x \), the area is \( 8(7 + x) \).

Answer:

Assuming the correct option is the one that represents \( 8(7 + x) \) (for example, if option D is \( 8(7 + x) \) or similar), the answer would be the option with the expression \( 8(7 + x) \) (or its expanded form \( 56 + 8x \)). If we consider the visible option A is \( 15 + x \) which is incorrect, and the correct formula gives \( 8(7 + x) \), so the answer is the option (e.g., D) that has \( 8(7 + x) \).