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

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. Write two different expressions giving the perimeter of the donkey’s pen.
b. Choose a value for a that is greater than 5 and less than 15. Evaluate the
perimeter of the pen for that value, using one of the expressions that you
wrote.
c. Explain why you used that expression to evaluate the perimeter of the
donkey’s pen.

GPT-4o mini · Answer

a. The perimeter $ P $ of a rectangle can be calculated using two different expressions based on its length $ a $ and width $ b $. The two expressions for the perimeter of A’Leila's donkey pen are: 1. $ P = 2a + 2b $ 2. $ P = 2(a + b) $ b. Let's choose a value for $ a $ that is greater than 5 and less than 15. For example, let's select $ a = 10 $ yards. To evaluate the perimeter of the pen, we need a value for $ b $. Let's say $ b = 8 $ yards. Now we can substitute the values of $ a $ and $ b $ into one of the expressions. We'll use the first expression: $$ P = 2a + 2b = 2(10) + 2(8) = 20 + 16 = 36 \text{ yards} $$ c. I used the first expression $ P = 2a + 2b $ because it straightforwardly shows how the perimeter is calculated by explicitly adding the contributions from both sides $ a $ and $ b $. This expression allows for clear substitution of the values for $ a $ and $ b $ to directly compute the total perimeter. It enhances understanding of the relationship between the sides and the overall perimeter of the rectangle.