Question

question 14
consider the rectangle depicted below.
which of the following computes the area of the rectangle?
image of a rectangle with base labeled ( x ) and height labeled ( y )
options:

• ( 2xy )
• ( 2x + 2y )
• ( 4xy )
• nothing in this list is correct.
• ( x + y )

Explanation:

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

The area of a rectangle is given by the formula \( A = \text{length} \times \text{width} \). In this case, the length is \( x \) and the width is \( y \), so the area should be \( A = x \times y = xy \).

Step2: Analyze the given options.

• Option \( 2xy \): This is not equal to \( xy \), so it's incorrect.
• Option \( 2x + 2y \): This is the formula for the perimeter of a rectangle (\( P = 2(\text{length} + \text{width}) = 2x + 2y \)), not the area, so it's incorrect.
• Option \( 4xy \): This is not equal to \( xy \), so it's incorrect.
• Option \( x + y \): This is just the sum of the length and width, not the area, so it's incorrect.
• Option "Nothing in this list is correct": Since the correct area formula \( xy \) is not among the first four options, this option is correct.

Answer:

Nothing in this list is correct.