Answer: The length and breadth of the rectangle are 15 feet and 6 feet respectively.
Step-by-step explanation: Given that a the length of a rectangle is 9 feet less than four times its width. its area is 90 square feet.
We are to determine the length and breadth of the rectangle algebraically.
Let, 'l' and 'w' represents the length and breadth of the rectangle.
Then, according to the given information, we have

We know that the area of a rectangle is equal to the product of its length and breadth.
So, the area of the given rectangle will be

Since the width of the rectangle cannot be negative, so w = 6 feet.
The length is l = 4w - 9 = 4 × 6 - 9 = 24 - 9 = 15 feet.
Thus, the length and breadth of the rectangle are 15 feet and 6 feet respectively.