A’Leila is building a pen for her pet donkey. The pen is a rectangle with one side

Question

measuring b yards and the adjacent side measuring a yards. A’Leila knows that
a-1/3b

Write two different expressions giving the perimeter of the donkey’s pen

Answer 1

The perimeter \( P \) of a rectangle can be calculated using the formula:

\[ P = 2 \times (\text{length} + \text{width}) \]

In this case, the length and width of the pen are \( b \) yards and \( a \) yards, respectively.

1. Using the standard perimeter formula:

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

2. Since it is given that \( a = \frac{1}{3}b \), we can use this relationship to express the perimeter in terms of \( b \):

Substituting \( a \) into the perimeter formula:

\[ P = 2\left(b + \frac{1}{3}b\right) = 2\left(\frac{3}{3}b + \frac{1}{3}b\right) = 2\left(\frac{4}{3}b\right) = \frac{8}{3}b \]

So, the two different expressions giving the perimeter of the donkey’s pen are:

1. \( P = 2(b + a) \)
2. \( P = \frac{8}{3}b \) (using \( a = \frac{1}{3}b \))