Final answer:
To find the length and width of the rectangle, we used the provided relationship between the two dimensions and the perimeter. Solving the resulting equation, we found the width to be approximately 5.33 meters and the length to be approximately 15.67 meters.
Step-by-step explanation:
The question involves finding the length and width of a rectangle when given the perimeter and a relationship between the length and width. Let's denote the width of the rectangle as w meters and the length as l meters. According to the problem, the length is five more than twice the width, which can be written as l = 2w + 5. The perimeter of a rectangle is given by P = 2l + 2w. The perimeter is stated to be 42 meters, so we substitute the expression for l into the perimeter equation and solve for w:
- P = 2l + 2w = 42
- Substitute l: 42 = 2(2w + 5) + 2w
- 42 = 4w + 10 + 2w
- 42 = 6w + 10
- 32 = 6w
- w = 32/6
- w = 5.33 (to two decimal places)
- Find l: l = 2(5.33) + 5 = 10.67 + 5
- l = 15.67 (to two decimal places)
Therefore, the sides of the rectangle are approximately 5.33 meters (width) and 15.67 meters (length).