A'lella is building a pen for her pet donkey. The pen is a rectangle with one side measuring b yards and the adjacent side measuring a yards. A'Lella knows that a=1/3b
a. Write two different expressions giving the perimeter of the donkey's pen.
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.
c. Explain why you used that expression to evaluate the perimeter of the donkey's pen.
a. The two different expressions giving the perimeter of the donkey's pen can be derived from the formula for the perimeter of a rectangle, P = 2a + 2b.
Expression 1: P = 2a + 2b = 2(1/3b) + 2b = (2/3)b + 2b = (8/3)b
Expression 2: Since a = 1/3b, we can substitute this value into the formula for the perimeter:
P = 2a + 2b = 2(1/3b) + 2b = (2/3)b + 2b = (8/3)b
b. Let's choose a value for a that is greater than 5 and less than 15. Let's say a = 6. To find the corresponding value of b, we'll use a = 1/3b:
6 = 1/3b
b = 6 * 3
b = 18
Using Expression 1:
P = (8/3)*18 = 48 yards (rounded to the nearest whole number)
c. I chose to use Expression 1 to evaluate the perimeter of the donkey's pen because it is derived from the given relationship between a and b (a = 1/3b). This ensures that the formula used to calculate the perimeter is consistent with the given information.