a. To find the perimeter of a rectangle, the formula is given by:
Since A’Leila knows that , we can express in terms of :
Now we can write a second expression for the perimeter using this substitution:
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Using the original dimensions:
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Using the relationship between and :
Substituting into the perimeter formula:
So, the two expressions for the perimeter are:
b. Let's choose a value for :
Let (which is greater than 5 and less than 15).
Now, we can evaluate the perimeter using the second expression :
c. I chose the expression to evaluate the perimeter of the donkey’s pen because it provides a direct relationship between the perimeter and the measurement of one side of the rectangle, . Since the problem specifies that can be conveniently chosen, this expression simplifies the calculation and eliminates the need to calculate before finding the perimeter. This makes it easier to quickly determine the perimeter based on the chosen value of .