Answer:
12 ft by 24 ft
Explanation:
1. Let's assume the width of the den is "x" feet. 2. According to the given information, the length of the den is 12 feet longer than its width, so the length can be represented as "x + 12" feet. 3. The area of a rectangle is calculated by multiplying its length by its width. We are given that the area of the den is 288 square feet. 4. We can set up the equation: (x)(x + 12) = 288. 5. Expanding the equation gives us x^2 + 12x = 288. 6. Rearranging the equation to have 0 on one side gives us x^2 + 12x - 288 = 0. 7. Now, we can solve this quadratic equation. We can factorize it or use the quadratic formula to find the values of x. 8. Factoring or using the quadratic formula, we find that x = 12 or x = -24. Since the width cannot be negative, we can discard the solution x = -24. 9. Therefore, the width of the den is 12 feet. 10. To find the length, we substitute the value of x into the equation x + 12. So, the length of the den is 12 + 12 = 24 feet. Therefore, the dimensions of Tony's den are 12 feet by 24 feet.