Question

12
2x + 3
a 14x + 15
b 24x + 3
c 24x + 36
d 4x + 30

Explanation:

Step1: Identify the shape and formula

The figure is a rectangle, and the area of a rectangle is given by \( A = \text{length} \times \text{width} \). Here, the length is \( 2x + 3 \) and the width is \( 12 \).

Step2: Apply the distributive property

Using the distributive property (also known as the distributive law of multiplication over addition), we multiply \( 12 \) by each term inside the parentheses:

$$ 12 \times (2x + 3) = 12 \times 2x + 12 \times 3 $$

Step3: Perform the multiplications

Calculate each product:

$$ 12 \times 2x = 24x \quad \text{and} \quad 12 \times 3 = 36 $$

Step4: Combine the terms

Combine the results to get the area:

$$ 24x + 36 $$

Answer:

C. \( 24x + 36 \)