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=(13)b
a
=
(
1
3
)
b
.
Write two different expressions giving the perimeter of the donkey’s pen.
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.
Explain why you used that expression to evaluate the perimeter of the donkey’s pen.
Two different expressions giving the perimeter of the donkey's pen are:
1) Perimeter = 2a + 2b
2) Perimeter = 2(a + b)
Let's choose a value for a = 8. Substituting this value into the expression 1) gives:
Perimeter = 2(8) + 2b
= 16 + 2b
Now let's evaluate the perimeter for b = 10:
Perimeter = 16 + 2(10)
= 16 + 20
= 36
We used the expression 1) to evaluate the perimeter because it directly calculates the sum of all four sides of the pen. By substituting the given values of a and b into the expression, we can easily find the perimeter without any additional steps.