Answer:
6 inches by 8 inches or 8 inches by 6 inches.
Explanation:
So, we have a rectangular piece of paper, which means it has a length and a width. We don't know what those dimensions are yet, but we can use some information we have to figure it out.
We know that the perimeter of the rectangle is 28 inches. Perimeter means the total distance around the outside of the rectangle, so we need to add up all four sides. We can use an equation to represent this:
Perimeter = 2 x (length + width)
So, for our rectangle, we have:
28 = 2 x (length + width)
Now, we also know that the area of the rectangle is 40 square inches. Area means the amount of space inside the rectangle. We can use another equation to represent this:
Area = length x width
For our rectangle, we have:
40 = length x width
We can use these two equations together to solve for the length and width of the rectangle. One way to do this is to use the equation for perimeter to solve for one of the variables in terms of the other. For example, we can solve for length like this:
28 = 2 x (length + width)
14 = length + width
length = 14 - width
Now we can substitute this expression for length into the equation for area:
40 = length x width
40 = (14 - width) x width
Simplifying this equation, we get:
40 = 14w - w^2
Rearranging, we get a quadratic equation:
w^2 - 14w + 40 = 0
We can solve for w using the quadratic formula:
w = (14 ± sqrt(14^2 - 4 x 1 x 40)) / (2 x 1)
w = (14 ± sqrt(36)) / 2
We get two possible values of w: 6 and 8. If w is 6, then the corresponding length would be 8. If w is 8, then the corresponding length would be 6.
So, the dimensions of the paper could be either 6 inches by 8 inches, or 8 inches by 6 inches.