A’Leila 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.

Question

A’Leila knows that a=1/3b

a. Write two different expressions giving the perimeter of the donkey’s pen. Using variable “b” only.
+2
b.Use the value a=12. Evaluate the perimeter of the pen for that value, using one of the expressions that you wrote.
+2
c.(don’t answer)

give the real answer

Answer 1

a. Two different expressions for the perimeter of the donkey's pen using variable "b" only can be written as:

Expression 1: Perimeter = 2b + 2a
Substituting the value of "a" from the given equation, a=1/3b, into the expression: Perimeter = 2b + 2(1/3b) = 2b + 2/3b = (6b + 2)/3b

Expression 2: Perimeter = 2(b + a)
Substituting the value of "a" from the given equation, a=1/3b, into the expression: Perimeter = 2(b + 1/3b) = 2(4/3b) = 8/3b

b. Given the value of "a" as 12, we can substitute it into one of the expressions to evaluate the perimeter of the pen. Let's use Expression 1:

Perimeter = (6b + 2)/3b
Substituting a=12: Perimeter = (6b + 2)/3b = (6(12) + 2)/3(12) = (72 + 2)/36 = 74/36 = 37/18

Thus, evaluating the perimeter of the pen for a=12 using Expression 1 gives a result of 37/18.