Final answer:
Considering the dimensions of the watch face are 5/7 inch by 1/2 inch and the options do not reflect any additional measurement from a gold encasing, the dimensions of the watch face including the gold encasing are not represented in the provided options. The correct answer, based on the given information and available choices, would be the original size of the watch face: 5/7 inch by 1/2 inch.
Step-by-step explanation:
The dimensions of the watch face itself are given as 5/7 inch by 1/2 inch, but we must also consider the 13-inch gold encasing. The phrase '13 inch gold encasing' is somewhat ambiguous, as it could refer to the length of the gold that encases the watch, possibly measured all around the rectangle, or it could refer to an increment that should be added to the dimensions of the watch face.
However, none of the options provided (a, b, c, d) reflect the addition of any length to the given dimensions of the watch face to account for an encasing, which would presumably increase the total dimensions of the watch face.
Therefore, assuming there is no typo in the provided options, the dimensions with the encasing considered seem not to be included, and the answer must be based solely on the original dimensions of the watch face, which are 5/7 inch by 1/2 inch.