Final answer:
The correct equation to solve for the width X of the steel frame, considering the typo in the area given, is '11 × (6 - 2X) = 38', which represents the area of the frame. By solving this equation, the width X can be determined, though the provided options and the area mentioned in the question seem to contain a miscommunication.
Step-by-step explanation:
The question is asking to solve for the width of a steel frame with given dimensions and area. The correct equation to represent this situation is 11 × (6 - 2X) = 28, where X indicates the width of the frame on one side. You can visualize the frame as a large rectangle with length 11 cm and width 6 cm, and inside it a smaller rectangle being the picture or mirror that the frame surrounds. If the area of the picture or mirror is 28 cm², then the area covered by the frame is the total area minus the area of the picture. Here the total area would be 11 cm × 6 cm = 66 cm². We subtract 28 cm² to get the area the frame occupies, which is 38 cm².
To find the width X, we need to express the area of the frame in terms of X. Each side of the frame consists of two widths (top/bottom and left/right), so we can write the area as 11 cm times the total width, which is (6 cm - 2X), giving us the equation 11 × (6 - 2X) = 38. This accounts for the width on both sides of the length and the width of the frame.
By solving this equation, we can find the value of X that will give us the desired frame area. Please note that there might have been a typo in the question as the provided options and desired area do not seem to align with the actual problem setup which should yield 38 cm² for the frame area instead of 28 cm².