Bot 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. A'Leila knows that a = 1/3b.
a. Write two different expressions giving the perimeter of the donkey's pen.
b. Chose 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. Expressions for the perimeter of the pen can be written as:
- P = 2a + 2b (perimeter formula using the lengths of two adjacent sides)
- P = 2(a + b) (perimeter formula using the sum of all sides)
b. Let's choose a = 6.
Since a = 1/3b, we can substitute the value of a to find b:
6 = 1/3b
b = 6 * 3
b = 18
Now we can calculate the perimeter using one of the expressions:
P = 2(a + b)
P = 2(6 + 18)
P = 2 * 24
P = 48
So the perimeter of the pen is 48 units.
c. I used the expression P = 2(a + b) to evaluate the perimeter because it simplifies the calculation by directly adding the lengths of all sides together. The expression 2(a + b) is convenient when we know the specific values of a and b, making it easier to substitute them in and find the result.