Final answer:
To solve the problem, we set up equations based on the given relationships and calculated the width to be 6 feet and the length to be 11.5 feet for the wooden rectangular frame.
Step-by-step explanation:
Given that the length is half a foot shorter than twice the width and the perimeter is 35 feet, we can start by setting up equations to represent these relationships. Let w be the width and l be the length in feet of the wooden frame. Using the information provided:
- Length (l) = 2w - 0.5
- Perimeter (P) = 2l + 2w = 35 feet
First, we substitute the expression for the length into the perimeter equation:
- 35 = 2(2w - 0.5) + 2w
- 35 = 4w - 1 + 2w
- 35 = 6w - 1
- 35 + 1 = 6w
- 36 = 6w
- w = 6 feet
Now, we find the length by substituting the width back into the length's equation:
- l = 2(6) - 0.5
- l = 12 - 0.5
- l = 11.5 feet
The width is 6 feet and the length is 11.5 feet.