Final answer:
To find the width and length of the rectangle, set up a system of equations and solve for the variables. In this case, the width is 17 cm and the length is 21 cm.
Step-by-step explanation:
To find the measure of the rectangle's length and width, we can set up a system of equations. Let's say that the width of the rectangle is x cm. According to the problem, the length of the rectangle is 4 more than its width, so the length would be x + 4 cm.
The formula for the perimeter of a rectangle is P = 2(length + width). Substituting the values we have, we can set up the equation 76 = 2(x + 4 + x).
Solving this equation, we get 76 = 4x + 8. By subtracting 8 from both sides, we have 68 = 4x. Dividing both sides by 4, we find that x = 17. Therefore, the width of the rectangle is 17 cm and the length is x + 4, or 17 + 4, which is 21 cm.