Final answer:
The maximum width of the rectangle when the perimeter is less than 78 cm is 14 cm.
Step-by-step explanation:
To express the maximum width of the rectangle, we need to set up an inequality based on the given information. Let's assume the width of the rectangle is 'w' cm.
The length of the rectangle is 4 cm less than twice the width, so the length would be (2w - 4) cm.
The perimeter of a rectangle is given by the formula: P = 2(length + width).
We are told that the perimeter is less than 78 cm, so we can set up the inequality: 2((2w - 4) + w) < 78.
Simplifying the inequality, we get: 6w - 8 < 78.
Adding 8 to both sides gives us: 6w < 86. Dividing both sides by 6, we find: w < 14.33.
Since we are looking for an integer value, the maximum width of the rectangle when the perimeter is less than 78 cm is 14 cm.