Answer:
the width of the rectangle is 4 units
Explanation:
Let's assume the length of the rectangle is "L" units.
According to the problem, the width of the rectangle is 4 units less than the length, which means the width is (L - 4) units.
The area of the rectangle is given as 32 square units, so we can write:
Length x Width = Area
L x (L - 4) = 32
Expanding the equation, we get:
L^2 - 4L = 32
Bringing all the terms to one side, we get:
L^2 - 4L - 32 = 0
Now, we can solve this quadratic equation for "L" using factoring or the quadratic formula. Factoring gives:
(L - 8)(L + 4) = 0
This gives two possible solutions for "L":
L = 8 or L = -4
We can reject the negative solution, since length cannot be negative. Therefore, the length of the rectangle is 8 units.
Using the equation for the width we found earlier, we can calculate the width of the rectangle as:
Width = L - 4 = 8 - 4 = 4 units.