Question

a rectangle has a width represented by the expression 2y and a length represented by 12y - 5. which expression represents the area of the rectangle? 12y² - 5y 24y² - 10y 24y - 10 28y - 10

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, i.e., \( A=\text{length} \times \text{width} \).

Step2: Substitute the given expressions for length and width

Given that the width is \( 2y \) and the length is \( 12y - 5 \), we substitute these into the formula: \( A=(2y)\times(12y - 5) \).

Step3: Apply the distributive property (FOIL method)

Using the distributive property \( a(b + c)=ab+ac \), we have:
\( (2y)\times(12y-5)=2y\times12y-2y\times5 \)

Step4: Simplify the terms

Simplify each term: \( 2y\times12y = 24y^{2} \) and \( 2y\times5=10y \). So the area is \( 24y^{2}-10y \).

Answer:

B. \( 24y^{2}-10y \) (assuming the options are labeled as A: \( 12y^{2}-5y \), B: \( 24y^{2}-10y \), C: \( 24y - 10 \), D: \( 28y - 10 \))