To solve this problem, you first need to set up an equation based on the given information. Let's start by assuming the length of the rectangle is x ft. According to the problem, the width is 2 ft less than the length, which means the width is x - 2 ft.
The formula for the area of a rectangle is length multiplied by width, so the area equation can be written as:
Area = Length × Width
8 ft² = x ft × (x - 2) ft
Now, we can solve this quadratic equation to find the value of x (length). To do so, we need to expand and rearrange the equation:
8 ft² = x² - 2x
0 = x² - 2x - 8 ft²
To factorize the equation, we need to find two numbers that multiply to give -8 (the coefficient of x²) and add up to -2 (the coefficient of x).
The factors of -8 are:
-8 and 1
-4 and 2
4 and -2
8 and -1
Out of these pairs, the numbers that add up to -2 are -4 and 2. So, we can rewrite the equation as:
0 = (x - 4)(x + 2)
Using the zero product property, we can solve for x by setting each factor equal to zero:
x - 4 = 0 or x + 2 = 0
Solving these equations gives us:
x = 4 or x = -2
Since the length cannot be negative, we discard the solution x = -2. Therefore, the length of the rectangle is x = 4 ft.
To find the width, we substitute the length value back into the width equation:
Width = Length - 2
Width = 4 ft - 2 ft
Width = 2 ft
So, the length of the rectangle is 4 ft, and the width is 2 ft.