Final answer:
To find the length of the rectangle, we translated the given condition into the equation 10w - 26 for the length and solved the quadratic equation resulting from setting the area equal to 8804 square feet. We found the width to be 31 feet, and thus the length is 284 feet.
Step-by-step explanation:
To find the length of a rectangle where the length is 26 feet less than 10 times its width and the area is 8804 square feet, let's denote the width of the rectangle as w.
Then, the length would be 10w - 26 feet. Since the area of a rectangle is the product of its length and width, we can set up the following equation:
Area = Length × Width
8804 = (10w - 26) × w
Now, we solve this quadratic equation:
10w^2 - 26w - 8804 = 0
Using the quadratic formula or factoring (if possible), we find the value of w, and then we calculate the length by substituting w back into the expression 10w - 26.
In this case, w is found to be 31 feet, therefore the length is 10(31) - 26, which equals 310 - 26, resulting in a length of 284 feet.