The following table shows the length and width of a rectangle:
Length Width
Rectangle A 4x + 5 3x − 2
Which expression is the result of the perimeter of rectangle A and demonstrates the closure property?
14x + 6; the answer is a polynomial
14x + 6; the answer may or may not be a polynomial
2x + 6; the answer is a polynomial
2x + 6; the answer may or may not be a polynomial
2x + 6; the answer is a polynomial
The perimeter of a rectangle is calculated by adding up all four sides of the rectangle. In this case, the length of rectangle A is given as 4x + 5, and the width is given as 3x - 2.
To find the perimeter of rectangle A, we need to add up the four sides:
Perimeter = 2 * (length + width)
Substituting the given expressions for length and width into the formula, we get:
Perimeter = 2 * (4x + 5 + 3x - 2)
Simplifying the expression inside the parentheses, we have:
Perimeter = 2 * (7x + 3)
Distributing the 2 to both terms inside the parentheses, we get:
Perimeter = 14x + 6
Therefore, the expression that represents the result of the perimeter of rectangle A is 14x + 6. And since it is purely an algebraic expression, it is a polynomial. Thus, the correct answer is: 14x + 6; the answer is a polynomial.