Question

the area of this rectangle is $5x^2$. what does the coefficient 5 mean in terms of the problem?
width x
length 5x
a. the total area of the square is 5.
b. the width is 5 times the length.
c. the length is 5.
d. the length is 5 times the width.

Explanation:

Step1: Recall Rectangle Area Formula

The area of a rectangle is \( \text{length} \times \text{width} \). Given width \( x \) and length \( 5x \), area is \( 5x \times x = 5x^2 \), which matches the given area.

Step2: Analyze Each Option

• Option A: The figure is a rectangle, not a square, and area is \( 5x^2 \), not 5. Eliminate A.
• Option B: Width is \( x \), length is \( 5x \), so length is 5 times width, not vice versa. Eliminate B.
• Option C: Length is \( 5x \), not 5 (unless \( x = 1 \), but generally, length is \( 5x \)). Eliminate C.
• Option D: Length \( 5x \), width \( x \), so length is \( \frac{5x}{x}=5 \) times width. This is correct.

Answer:

D. The length is 5 times the width.