A'Leila is building a pen foe her pet donkey. The pen is a rectangle with one side measuring b yards and the adjacent side measuring a yards. A'Leila knows a = 1/3b. Write two different expressions giving the perimeter of the donkeys pen
Expression 1:
The perimeter of a rectangle is given by adding up all its sides. In this case, the perimeter is given by the sum of the length of one side (a), the length of the adjacent side (b), and the length of the other two sides (which are the same as a and b). Thus, the perimeter expression is:
Perimeter = a + b + a + b = 2a + 2b
Since a = 1/3b, we can substitute this value into our expression to get:
Perimeter = 2(1/3b) + 2b
Perimeter = 2/3b + 2b
Expression 2:
Alternatively, we can also write the perimeter expression in terms of just one variable. For example, we can express the length of the shorter side (a) in terms of the longer side (b). Since a = 1/3b, we can solve for a as follows:
a = 1/3b
3a = b
b = 3a
We can substitute this value of b into the perimeter expression to get:
Perimeter = a + b + a + b
Perimeter = a + 3a + a + 3a
Perimeter = 6a
Therefore, we have two different expressions for the perimeter of the donkey's pen:
1) Perimeter = 2/3b + 2b
2) Perimeter = 6a