Answer:
Width = 2 cm; Length = 9 cm
Explanation:
Formula for the perimeter of a rectangle:
The formula for the perimeter of a rectangle is given by:
P = 2L + 2W, where
- P is the perimeter,
- L is the length,
- and W is the width.
Equation relating the rectangle's width and length:
Since the rectangle's length is 1 cm more than four times its width, we can represent this with the following equation:
L = 4W + 1
Finding the width:
Since the rectangles perimeter is 22 cm, we can find its width by substituting 22 for P and 4W + 1 for L in the rectangle perimeter formula:
22 = 2(4W + 1) + 2W
22 = 8W + 2 + 2W
(22 = 10W + 2) - 2
(20 = 10W) / 10
2 = W
Thus, the rectangle's width is 2 cm.
Finding the length:
Now we can find the length by adding 1 to four times the width (2 cm):
L = 4(2) + 1
L = 8 + 1
L = 9
Thus, the length is 9 cm.