Question

consider the rectangle depicted below. which of the following computes the area of the rectangle? rectangle image with base labeled x and height labeled y options: ( x + y ), ( 2xy ), nothing in this list is correct, ( 4xy ), ( 2x + 2y )

Explanation:

Step1: Recall the formula for the area of a rectangle.

The area \( A \) of a rectangle is given by the product of its length and width. If the length is \( x \) and the width is \( y \), then the area formula is \( A = x \times y = xy \).

Step2: Analyze the given options.

• Option \( x + y \): This is the sum of the length and width, which is the formula for neither area nor perimeter (perimeter is \( 2x + 2y \)). So this is incorrect.
• Option \( 2xy \): This is not the standard area formula for a rectangle. The area is \( xy \), so this is incorrect.
• Option "Nothing in this list is correct": We will check other options first.
• Option \( 4xy \): This is also not the area formula for a rectangle. Incorrect.
• Option \( 2x + 2y \): This is the formula for the perimeter of a rectangle (sum of all sides), not the area. Incorrect.

Since none of the provided options (other than the "nothing correct" option) match the area formula \( xy \), we conclude that the correct option is the one stating "Nothing in this list is correct."

Answer:

Nothing in this list is correct.