Question

select the correct answer. in a floor plan, the length, l, of a rectangular room is twice its width, w. the perimeter of the room must be greater than 72 feet. which inequality can be used to find all possible widths of the room, in feet? a. 6w > 72 b. 6w < 72 c. 3w > 72 d. 3w < 72 (with an image of a rectangle labeled length (l) and width (w))

Explanation:

Step1: Define length in terms of width

Length \( l = 2w \) (since length is twice width).

Step2: Recall perimeter formula for rectangle

Perimeter \( P = 2(l + w) \). Substitute \( l = 2w \): \( P = 2(2w + w) = 2(3w) = 6w \).

Step3: Set up inequality for perimeter

Perimeter must be greater than 72, so \( 6w > 72 \).

Answer:

A. \( 6w > 72 \)