Final answer:
To find the dimensions of a deck with three sides of railings using 28 meters of material, one side is left unrailed. The dimensions need to satisfy the equation 2L + W = 28. Option D, 12m x 4m, is the only combination satisfying this equation.
Step-by-step explanation:
The question is about finding the dimensions of a rectangle that would use exactly 28 meters of railing on three of its sides. To solve this problem, let's denote the length of the deck as L and the width of the deck as W. Since railings are placed on only three sides, the total length of the railings will be L + L + W, which should equal the 28 meters available. Thus, the equation to solve is 2L + W = 28 meters.
Reviewing each option:
- 7m x 7m: 2(7) + 7 = 21, not 28 meters.
- 10m x 6m: 2(10) + 6 = 26, not 28 meters.
- 8m x 5m: 2(8) + 5 = 21, not 28 meters.
- 12m x 4m: 2(12) + 4 = 28 meters. This is the correct answer.
Therefore, the dimensions of the deck that would utilize the maximum 28 meters of railing on three sides are 12m x 4m, which corresponds to option D.