Will give !
the following table shows the length and width of a rectangle: length width rectangle a 3x + 5 2x − 3 which expression is the result of the perimeter of rectangle a and demonstrates the closure property?
a. 10x + 4; the answer is a polynomial
b. 2x + 4; the answer is a polynomial
c. 10x + 4; the answer may or may not be a polynomial
d. 2x + 4; the answer may or may not be a polynomial

a. 10x + 4; the answer is a polynomial

Step-by-step explanation:

The perimeter of a rectangle is the sum of the lengths of the 4 sides.

The closure property is that if you add polynomials, the sum is a polynomial.

A rectangle has two congruent lengths and two congruent widths.

Since the length of the rectangle is 3x + 5, there is another length of 3x + 5. The width is 2x - 3, so there is a second width of also 2x - 3.

Let's add the 4 sides together:

3x + 5 + 3x + 5 + 2x - 3 + 2x - 3 =

= 3x + 3x + 2x + 2x + 5 + 5 - 3 - 3

= 10x + 4

The perimeter is 10x + 4. Each side length is a polynomial, and the sum of the all the side length is also a polynomial. This shows there is closure for the addition of polynomials.

a. 10x + 4; the answer is a polynomial

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.

step-by-step explanation: