Leah is building a pen for her donkey. The pen is a rectangle with one side, measuring b yards and the adjacent side measuring a yards Leah knows that an equals 1/3 of b write two different expressions giving the perimeter of the donkeys pen
Expression 1:
Since Leah knows that a equals 1/3 of b, we can substitute a into the equation for b to get a = (1/3)b.
The perimeter of the pen is the sum of all four sides, which can be expressed as: P = 2a + 2b.
Substituting a = (1/3)b in the expression for P, we get: P = 2(1/3)b + 2b.
Simplifying this expression, we have: P = (2/3)b + 2b.
Expression 1 for the perimeter of the donkey's pen is: P = (2/3)b + 2b.
Expression 2:
Alternatively, we can express a in terms of b directly. Since a is 1/3 of b, we can write a = (1/3)b.
Again, the perimeter of the pen is the sum of all four sides, which can be expressed as: P = 2a + 2b.
Substituting a = (1/3)b in the expression for P, we get: P = 2(1/3)b + 2b.
Simplifying this expression, we have: P = (2/3)b + 2b.
Expression 2 for the perimeter of the donkey's pen is also: P = (2/3)b + 2b.