Final answer:
The width of the frame must be greater than 35 inches for the perimeter to be greater than 154 inches.
Step-by-step explanation:
To find the dimensions of the picture frame, you can set up a system of equations. Let x be the width of the frame. According to the problem, the length is 7 inches more than the width, so the length is x+7 inches. The perimeter of a rectangle is the sum of all its sides, which in this case is 2(x+x+7) inches. Set this expression greater than 154 and solve for x.
2(x+x+7) > 154
2(2x+7) > 154
4x+14 > 154
4x > 140
x > 35
Therefore, the width of the frame must be greater than 35 inches for the perimeter to be greater than 154 inches.