Final answer:
The width of the rectangle is 3 cm and the length is 19 cm.
Step-by-step explanation:
Let's define the width of the rectangle as 'w'. According to the problem, the length is 7 cm more than 4 times the width, so the length can be written as '4w + 7'.
The perimeter of a rectangle is calculated by adding twice the length to twice the width. In this case, the perimeter is given as 44 cm, so we can set up the equation: 2(4w + 7) + 2w = 44.
Simplifying the equation, we get 8w + 14 + 2w = 44. Combining like terms, we have 10w + 14 = 44. Subtracting 14 from both sides gives us 10w = 30. Finally, dividing both sides by 10, we find that w = 3.
Therefore, the width of the rectangle is 3 cm, and the length can be found by plugging in this value into '4w + 7'. The length is 4(3) + 7 = 12 + 7 = 19 cm.