Answer:
The dimensions of the rectangle are approximately 8.54 units by 3.54 units.
Explanation:
Let's start by using algebra to represent the information given in the problem.
Let L be the length of the rectangle.
Then, the width of the rectangle is 5 units less than the length, which means the width can be expressed as L - 5.
The area of a rectangle is given by the formula A = L * W, where A is the area, L is the length, and W is the width. In this case, we are given that the area is 36 square units. So we can write:
A = L * (L - 5)
36 = L * (L - 5)
Expanding the right-hand side of the equation, we get:
36 = L^2 - 5L
Moving all the terms to the left-hand side of the equation, we get:
L^2 - 5L - 36 = 0
Now we can use the quadratic formula to solve for L:
L = (-(-5) ± sqrt((-5)^2 - 4(1)(-36))) / (2(1))
Simplifying this expression, we get:
L = (5 ± sqrt(229)) / 2
We can discard the negative solution since the length of a rectangle cannot be negative.
So, the length of the rectangle is approximately 8.54 units (rounded to two decimal places).
To find the width, we can substitute this value of L into the expression we derived earlier for the width:
W = L - 5
W = 8.54 - 5
W ≈ 3.54 units (rounded to two decimal places)
Therefore, the dimensions of the rectangle are approximately 8.54 units by 3.54 units.