Final answer:
By setting up equations from the given information, the width of the picture is found to be 28 inches and the length is 36.75 inches. These dimensions are not reflected in the multiple-choice options provided, suggesting a possible error in the options.
Step-by-step explanation:
To find the dimensions of the picture, we need to first set up equations based on the information given. The length (L) of the picture is 19.25 inches shorter than twice the width (W), so we can write this as L = 2W - 19.25. Also, we know that the perimeter (P) of a rectangle is the sum of twice its length and twice its width, expressed as P = 2L + 2W. Substituting the given perimeter of 129.5 inches, we get the equation 129.5 = 2(2W - 19.25) + 2W.
Simplifying the equation gives us 129.5 = 4W - 38.5 + 2W, which further simplifies to 6W = 168. This yields W = 28 inches. Now, we substitute the value of W into the first equation to find L: L = 2(28) - 19.25, resulting in L = 36.75 inches.
Thus, the dimensions of the picture are 28 inches in width and 36.75 inches in length. This matches none of the options given, indicating that there may be a typo or error within the options provided.