Final answer:
The width of the rectangle is 7 ft, and the length is 11 ft.
Step-by-step explanation:
Let's assign the width of the rectangle as w. According to the given information, the length of the rectangle is 10 ft less than three times the width, so the length can be represented as 3w - 10.
The formula for the area of a rectangle is length multiplied by width. Therefore, we have the equation: (3w - 10) * w = 77.
To solve this equation, we can multiply the terms: 3w^2 - 10w = 77. Rearranging the terms, we have: 3w^2 - 10w - 77 = 0.
Next, we can factorize the equation: (3w + 11)(w - 7) = 0. Therefore, w = 7 or w = -11/3. Since the width cannot be negative, we can discard w = -11/3.
So, the width of the rectangle is 7 ft, and the length is
3w - 10 = 3(7) - 10
= 21 - 10
= 11 ft.