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.
.
1. Write two different expressions giving the perimeter of the donkey’s pen.
2. 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.
3. Explain why you used that expression to evaluate the perimeter of the
donkey’s pen
1. Expressions for the perimeter of the donkey's pen:
a) Perimeter = 2a + 2b
b) Perimeter = 4a
2. Let's choose a value for a as 6. Since a = 1/3b, we can substitute this value in the equation and solve for b:
6 = 1/3b
b = 18
Using the expression from part (a), we can plug in the values for a and b:
Perimeter = 2a + 2b
Perimeter = 2(6) + 2(18)
Perimeter = 12 + 36
Perimeter = 48 yards
Therefore, the perimeter of the donkey's pen for a value of a = 6 is 48 yards.
3. I used the expression from part (a) to evaluate the perimeter of the donkey's pen because it takes into account both sides of the rectangle, a and b. By calculating 2a + 2b, we ensure that we are considering the lengths of both sides of the pen, which gives us the accurate perimeter measurement.