Answer:
Let's assume that the length of the rectangle is "x" units.
According to the problem, the width of the rectangle is 1 unit less than the length. Therefore, the width can be represented as (x-1) units.
We know that the area of a rectangle is equal to its length multiplied by its width. So, the area of this rectangle is given as 56 square units.
Using the formula for the area of a rectangle, we can write:
Length x Width = Area
x(x-1) = 56
Expanding the left side of the equation, we get:
x^2 - x = 56
Rearranging the terms, we get a quadratic equation:
x^2 - x - 56 = 0
Now we can solve for x by factoring the quadratic equation:
(x-8)(x+7) = 0
This gives us two possible values for x: x=8 and x=-7.
Since length cannot be negative, we reject x=-7 and conclude that the length of the rectangle is 8 units.
Therefore, the length of the rectangle is 8 units and the width is (8-1) = 7 units.
Explanation: