Question

the area of this rectangle is ( 3x^2 ). what does the coefficient 3 mean in terms of the problem?
image: rectangle labeled width ( x ) and length ( 3x )

a. the length is 3 times the width.

b. the length is 3.

c. the total area of the square is 3.

d. the width is 3 times the length.

Explanation:

• Analyze Option A: The width is \( x \) and the length is \( 3x \). So, length \( = 3\times \) width (since \( 3x = 3\times x \)). This means the length is 3 times the width.
• Analyze Option B: The length is \( 3x \), not 3 (unless \( x = 1 \), but generally, length depends on \( x \)). So B is incorrect.
• Analyze Option C: The area is \( 3x^{2} \), not 3 (unless \( x^{2}=1 \), but area depends on \( x \)). So C is incorrect.
• Analyze Option D: Width is \( x \), length is \( 3x \), so width is \( \frac{1}{3} \) of length, not 3 times. So D is incorrect.

Answer:

A. The length is 3 times the width.