Final answer:
To write an equation in standard form, use the formula for perimeter and set it equal to the given rectangle's perimeter. Then, solve for the other variables to find possible lengths and widths.
Step-by-step explanation:
To write an equation in standard form that models the possible lengths and widths of a rectangle with the same perimeter as a rectangle that is 10 feet wide and 20 feet long, we need to understand that the perimeter is calculated by adding the lengths of all sides of the rectangle. In this case, the perimeter is 2*(l+w), where l is the length and w is the width. Given that the rectangle is 10 ft wide and 20 ft long, and the perimeter of the rectangle is the same, we can set up the equation: 2*(l+10) = 2*(20+w) to represent the relationship. Expanding and simplifying this equation will yield the equation in standard form.
To create a table of possible lengths and widths of the rectangle, we can choose different values for l and solve the equation to find the corresponding values of w. For example:
- If we choose l = 15, we can solve the equation to find w = 15.
- If we choose l = 25, we can solve the equation to find w = 5.
- If we choose l = 30, we can solve the equation to find w = 0.
- If we choose l = 35, we can solve the equation to find w = -5.
- If we choose l = 40, we can solve the equation to find w = -10.
These are five possible lengths and widths of the rectangle that satisfy the equation and have the same perimeter as the given rectangle.
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