Question

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
Use the value a=12. Evaluate the perimeter of the pen for that value, using one of the expressions that you wrote.

Answer 1

To find the perimeter of the rectangular pen, we can use the formula for the perimeter \( P \) of a rectangle, which is given by:

\[
P = 2(a + b)
\]

Given that \( a = \frac{1}{3}b \) and that \( a = 12 \), we can substitute \( a \) into the equation for \( b \).

Starting from the equation for \( a \):

\[
a = \frac{1}{3}b
\]

Substituting the value of \( a \):

\[
12 = \frac{1}{3}b
\]

To find \( b \), we can multiply both sides by 3:

\[
b = 3 \times 12 = 36
\]

Now we have both dimensions of the pen: \( a = 12 \) yards and \( b = 36 \) yards.

Now we can substitute these values into the perimeter formula:

\[
P = 2(a + b) = 2(12 + 36)
\]

Calculating inside the parentheses:

\[
12 + 36 = 48
\]

Now multiply by 2:

\[
P = 2 \times 48 = 96
\]

Thus, the perimeter of the pen is \( \boxed{96} \) yards.