Question

examine the rectangle.
diagram: rectangle with length labeled 5x and width labeled 2x + 4
which represents the area of this rectangle?
a. 10x + 4
b. 7x + 4
c. 10x² + 20x
d. 10x² + 4
e. 7x² + 20x

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \). Here, the length is \( 5x \) and the width is \( 2x + 4 \). So we need to calculate \( 5x \times (2x + 4) \).

Step2: Apply distributive property (FOIL for monomial and binomial)

Using the distributive property \( a(b + c)=ab+ac \), where \( a = 5x \), \( b = 2x \), and \( c = 4 \), we get:
\( 5x \times 2x + 5x \times 4 \)

Step3: Simplify each term

For the first term, \( 5x \times 2x = 10x^2 \) (since \( x \times x = x^2 \) and \( 5\times2 = 10 \)). For the second term, \( 5x \times 4 = 20x \). Combining these terms, we have \( 10x^2 + 20x \).

Answer:

C. \( 10x^2 + 20x \)