Question

Mr.bonifacio cuts different sizes of rectangular plywood to be used in the furniture that he makes some of these rectangular plywood are described below.

- Plywood1: The length of the plywood is twice its width and the area is 4.5sq ft.
- Plywood2: The length of the plywood is 1.4 less than twice its width and the area is 16sq ft.
- Plywood3: The perimeter of the plywood is 10ft. and its area is 6sq ft.

Which of the solutions or roots obtained represents the width of each plywood? Explain your answer.

Answer 1

The widths of three pieces of rectangular plywood can be determined by setting up equations based on their described relationships between length, width, area, and perimeter, then solving for width while disregarding negative roots.

Step-by-step explanation:

The task is to determine the widths of three pieces of rectangular plywood based on the given descriptions:

1. Plywood 1: Length is twice its width, with an area of 4.5 sq ft. This gives us an equation L = 2W and Area (A) = L x W = 4.5. Therefore, W (width) can be found by setting up the equation 2W x W = 4.5 and solving for W.
   
   
2. Plywood 2: Length is 1.4 ft less than twice its width, with an area of 16 sq ft. The equations would be L = 2W - 1.4 and A = LW = 16, which can be used to find W by substituting the expression for L into the area equation.
   
   
3. Plywood 3: Perimeter is 10 ft, and area is 6 sq ft. We know that the perimeter (P) of a rectangle is 2L + 2W = 10 ft and the area (A) is L x W = 6 sq ft. By setting up the two equations, we can solve for both L and W.

The solutions or roots obtained from these equations will represent the width of each plywood, with the understanding that any negative roots should be disregarded, as width cannot be negative in this context. Additionally, the correct width is determined by the requirement that it fits the constraints given for both area and perimeter.