A rectangle has length 8 cm and width w. Which function expresses its area A(w)?

A rectangle has length 8 cm and width w. Which function expresses its area A(w)?

• A. A(w) = w^2
• B. A(w) = 8w
• C. A(w) = 8 + w
• D. A(w) = 8 - w

Answer: (B)

The amount of space inside a rectangle comes from multiplying its two side lengths. With length 8 cm and width w cm, the area is A(w) = 8 × w = 8w square centimeters. This matches how area scales: it grows in proportion to the width while the length stays fixed. The other forms don’t fit because they either multiply the wrong dimensions or add/subtract rather than multiply. Width squared would imply using the width for both sides, which isn’t the case here, and adding or subtracting the sides would not give area.

The amount of space inside a rectangle comes from multiplying its two side lengths. With length 8 cm and width w cm, the area is A(w) = 8 × w = 8w square centimeters. This matches how area scales: it grows in proportion to the width while the length stays fixed.

The other forms don’t fit because they either multiply the wrong dimensions or add/subtract rather than multiply. Width squared would imply using the width for both sides, which isn’t the case here, and adding or subtracting the sides would not give area.