The width of a rectangle is 1 ft. less than the length. The area is 2ft^2. Find the length and the width.
Do you mean 2 square feet? If so, than the dimensions must be 1 foot by 2 feet.
If you mean 2 feet squared, then the area is 4 square feet.
To find the length and width of the rectangle, let's use the given information and solve the problem step by step.
Let's assume the length of the rectangle is represented by the variable 'L' (in feet).
According to the problem, the width of the rectangle is 1 ft less than the length. Therefore, the width can be represented by 'L - 1' (in feet).
The area of a rectangle is given by the product of its length and width. In this case, the area is given as 2 ft^2. So, we can set up the following equation:
Length * Width = Area
Substituting the values, we get:
L * (L - 1) = 2
Now, let's solve this equation to find the value of 'L' (length).
Expanding the equation:
L^2 - L = 2
Rearranging the terms:
L^2 - L - 2 = 0
Now, we can solve the equation by factoring or using the quadratic formula. In this case, let's factor the equation:
(L - 2)(L + 1) = 0
Setting each factor equal to zero and solving for 'L', we get:
L - 2 = 0 --> L = 2
L + 1 = 0 --> L = -1 (discard this solution since length cannot be negative)
So, the length of the rectangle is 2 ft.
Now, to find the width, substitute the value of 'L' in the equation: Width = L - 1
Width = 2 - 1 = 1 ft.
Therefore, the length of the rectangle is 2 ft and the width is 1 ft.