b. Choose a value for a that is greater than 5 and less than 15. Evaluate the perimeter of the pen for that value, using one of the expressions that you wrote.
Let's choose a = 10.
Using the expression P = 2a + 30, substitute a = 10:
P = 2(10) + 30
P = 20 + 30
P = 50
Therefore, when a = 10, the perimeter of the pen is 50.
c. Explain why you used that expression to evaluate the perimeter of the donkey’s pen.
I used the expression P = 2a + 30 to evaluate the perimeter of the donkey's pen because the expression represents the formula for calculating the perimeter of a rectangular pen.
The formula for the perimeter of a rectangle is P = 2(length + width). In this case, the length of the pen is represented by "a" and the width is a fixed value of 15. To calculate the perimeter, we need to add up the lengths of all four sides of the pen, which is why we multiply the length by 2 in the expression.
The additional 30 in the expression accounts for the fixed width of 15 on two sides of the pen, so we add 15 + 15 = 30. This ensures that the length of the pen is correctly accounted for in the perimeter calculation.
By using this expression, we can plug in different values for "a" and get the corresponding perimeter of the pen. This allows us to evaluate and compare the perimeters for different values of "a" and choose the desired value within the given range.