Final answer:
To find the length and width of the rectangular room, set up a system of equations using the given information. Solve the quadratic equation to find the width of the room, then the length can be calculated by subtracting 2 from the width.
Step-by-step explanation:
To find the length and width of the room, we can set up a system of equations based on the given information. Let's assume the width of the room is x feet. According to the problem, the length of the room is 2 feet less than the width, so the length would be (x - 2) feet.
Now we can set up an equation to find the value of x. The area of a rectangle is given by the formula A = length x width. Since the area is given as 575 square feet, we can write:
575 = (x - 2)x
Simplifying the equation, we have:
575 = x^2 - 2x
Now we can solve this quadratic equation for x. Rearranging the equation, we get:
x^2 - 2x - 575 = 0
Factoring this quadratic equation or using the quadratic formula will give us the values of x, which are the width of the room. The lengths would be (x - 2) feet.