Final answer:
Using the Pythagorean theorem, we can calculate the dimensions of the plywood if the width is w, then the length is 2w and the diagonal is w + 1. By solving the equation, we find that the length of the plywood's diagonal is 1.5 feet.
Step-by-step explanation:
To solve the question about the rectangular piece of plywood, we must use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (often called legs). The problem gives us two pieces of information:
- The diagonal is one foot more than the width.
- The length is two times the width.
If we let w represent the width, then the diagonal is w + 1 feet, and the length is 2w. Using the Pythagorean theorem:
(width)^2 + (length)^2 = (diagonal)^2
w^2 + (2w)^2 = (w + 1)^2
w^2 + 4w^2 = w^2 + 2w + 1
5w^2 = w^2 + 2w + 1
4w^2 = 2w + 1
4w^2 - 2w - 1 = 0
Now we can solve this quadratic equation for w, which then lets us find the length and the diagonal.
However, if we assume it's a right triangle, we can simplify the steps as follows:
(2w)^2 + w^2 = (w + 1)^2
5w^2 = w^2 + 2w + 1
4w^2 = 2w + 1
Solving for w, we get that w = 1/2. Hence, the diagonal of the plywood is:
Diagonal = w + 1 = 1/2 + 1 = 1.5 feet
The length of the plywood's diagonal is therefore 1.5 feet.