Final answer:
To find the width and length of the rectangle, assign variables to represent them and set up the perimeter equation. Solve the equation to find the width and length.
Step-by-step explanation:
To solve this problem, we can assign variables to represent the width and length of the rectangle. Let's say the width is 'w' cm.
According to the given information, the length of the rectangle is 9 cm less than 4 times the width. So, the length can be expressed as: 4w - 9 cm.
The perimeter of a rectangle is found by adding up all its sides. In this case, it is given to be 142 cm.
Using the formula for the perimeter of a rectangle, which is P = 2(w + l), we can substitute the values and solve for the width and length of the rectangle.
142 = 2(w + 4w - 9)
Simplifying the equation, we get:
142 = 2(5w - 9)
71 = 5w - 9
5w = 80
w = 16
So, the width of the rectangle is 16 cm.
Substituting this value back into the expression for the length, we get:
length = 4w - 9 = 4(16) - 9 = 64 - 9 = 55 cm.
Therefore, the width of the rectangle is 16 cm and the length is 55 cm.