Final answer:
The width that will give Jorge's box the largest possible volume, when rounded to the nearest tenth, is 5.7 cm. This is found by graphing the volume function with respect to width and determining the maximum value.
Step-by-step explanation:
Jorge is tasked with building a box in the shape of a rectangular prism, where its height is 2 cm more than its width, and the sum of the length, width, and height is 20 cm. To find the width that would give the box the largest possible volume, we can set up an equation with one variable, in this case the width which we can denote as w.
Therefore, the height h will be w + 2 and the length l can be expressed as 20 - w - (w + 2) which simplifies to 18 - 2w. We can now express the volume V as a function of width w: V = w × (w + 2) × (18 - 2w).
Graph this function on a graphing calculator and find the width w that maximizes the volume. To round the width to the nearest tenth of a cm, choose the value that corresponds to the maximum point on the graph. After graphing, we find that the width leading to the maximum volume is approximately 5.7 cm, corresponding to option B.