Answer:
Explanation:
To find the dimensions of the rectangle, we'll use the formula for the area of a rectangle:
Area = Length × Breadth
In this case, the area is given as x² + 4x + 3, and the breadth is given as x - 2. We need to find the length.
Let the length of the rectangle be L.
Area = Length × Breadth
x² + 4x + 3 = L × (x - 2)
Now, we'll solve for L:
Step 1: Expand the right side of the equation.
x² + 4x + 3 = Lx - 2L
Step 2: Move all the terms to one side to set the equation to zero.
Lx - x² - 4x - 2L + 3 = 0
Step 3: Combine like terms.
Lx - x² - 4x + (3 - 2L) = 0
Step 4: To find the value of L, we need to set the equation equal to zero. However, this is a quadratic equation, and to solve for L, we'll set it in the factored form.
Step 5: Factor the quadratic equation.
(x - 1)(x - 3) = 0
Step 6: Set each factor to zero and solve for x.
x - 1 = 0 --> x = 1
x - 3 = 0 --> x = 3
Now that we have two possible values for x (x = 1 and x = 3), we can find the corresponding lengths of the rectangle:
For x = 1:
Length (L) = x = 1
Breadth = x - 2 = 1 - 2 = -1 (Note: The breadth cannot be negative, so this value is not valid.)
For x = 3:
Length (L) = x = 3
Breadth = x - 2 = 3 - 2 = 1
So, the valid dimensions of the rectangle are:
Length = 3 units
Breadth = 1 unit