Final answer:
The length of the mirror is 12 inches and the width is 5 1/3 inches.
Step-by-step explanation:
To find the dimensions of the mirror, we can set up an equation using the information given.
Let the length of the mirror be x. According to the problem, the width of the mirror is 4/9 times its length.
So, the width can be expressed as (4/9)x.
The area of the mirror is given as 576 square inches.
We can set up an equation using the formula for the area of a rectangle, which is length multiplied by width.
So, we have (4/9)x * x = 576.
Simplifying this equation, we get (4/9)x^2 = 576.
To solve for x, we can multiply both sides by (9/4) to get x^2 = 144, and then take the square root of both sides to get x = 12.
Therefore, the length of the mirror is 12 inches, and the width is (4/9) * 12 = 16/3 inches, or 5 1/3 inches.