Question

width of a rectangle is $w + 4$ and the length of the rectangle is $2w + 3$. which expression represents the area of the rectangle?
a. $2w^2 + 11w + 7$
b. $2w^2 + 5w + 7$
c. $2w^2 + 11w + 12$
d. $2w^2 + 9w + 12$

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by the product of its length and width, i.e., \( A=\text{length}\times\text{width} \). Here, length is \( 2w + 3 \) and width is \( w + 4 \), so we need to compute \( (2w + 3)(w + 4) \).

Step2: Apply distributive property (FOIL method)

First, multiply the First terms: \( 2w\times w = 2w^{2} \).
Then, the Outer terms: \( 2w\times4 = 8w \).
Next, the Inner terms: \( 3\times w = 3w \).
Finally, the Last terms: \( 3\times4 = 12 \).

Step3: Combine like terms

Combine the middle terms (\( 8w \) and \( 3w \)): \( 8w+3w = 11w \).
So, putting it all together: \( 2w^{2}+8w + 3w+12=2w^{2}+11w + 12 \).

Answer:

C. \( 2w^{2}+11w + 12 \)