Question

The perimeter of a rectangle is the sum of the lengths of its four sides. Which expression, where L = length and W = width, does not show this relationship?

A) 2(L + W)
B) 2L + 2W
C) L + W + L + W
D) 2/L

Answer 1

The correct answer is D) 2/L because it does not represent the perimeter of a rectangle. Options A, B, and C all correctly show this relationship as they sum the lengths of all four sides of the rectangle.

Step-by-step explanation:

The perimeter of a rectangle is the sum of the lengths of its four sides. Considering the expressions given where L represents the length and W represents the width, the correct expressions that show this relationship are 2(L + W), 2L + 2W, and L + W + L + W. These expressions all simplify to the same result (the total perimeter), by either adding the lengths and widths first and then multiplying by 2, or by summing twice the length and twice the width.

However, the expression 2/L does not represent the perimeter of a rectangle, as it suggests dividing 2 by the length (L), which doesn’t correspond to the concept of perimeter or any combination of the sides of a rectangle. Thus, expression D) 2/L is the one that does not show the relationship of a rectangle's perimeter.