Answer: Let's use algebra to find the length of the rectangle.
Let:
Length of the rectangle = L units
Width of the rectangle = (L - 6) units
The area of a rectangle is given by the formula: Area = Length * Width
Given that the area is seven square units, we can write the equation:
Area = L * (L - 6) = 7
Now, let's solve the equation for L:
L^2 - 6L = 7
Move all terms to one side:
L^2 - 6L - 7 = 0
Now, we have a quadratic equation in the form of Ax^2 + Bx + C = 0, where A = 1, B = -6, and C = -7. We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, we'll use factoring.
Factor the quadratic equation:
(L - 7)(L + 1) = 0
Now, set each factor equal to zero and solve for L:
L - 7 = 0
L = 7
L + 1 = 0
L = -1
Since the length of a rectangle cannot be negative, we discard the negative solution.
So, the length of the rectangle is 7 units.