Final answer:
The dimensions of the rectangle are a width of 23 cm and a length of 47 cm, which can be calculated by setting up equations from the perimeter and the given relationship between length and width.
Step-by-step explanation:
The question involves finding the dimensions of a rectangle when given the perimeter and a relationship between the length and width. To solve this problem, denote the width of the rectangle as w and the length as l. According to the problem, the perimeter (P) is 140 cm, and the length is 1 cm more than twice the width, which gives us the equations:
- P = 2l + 2w = 140 cm
- l = 2w + 1 cm
Substituting the second equation into the first, we get:
- 2(2w + 1) + 2w = 140
- 4w + 2 + 2w = 140
- 6w + 2 = 140
- 6w = 138
- w = 23 cm
Now, substituting the width back into the equation for the length, we find:
- l = 2(23) + 1
- l = 46 + 1
- l = 47 cm
Therefore, the dimensions of the rectangle are a width (w) of 23 cm and a length (l) of 47 cm.