A'Lelia 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'Lelia knows that a= 1/2b.
If A'Lelia knows that a = 1/2b, we can substitute this value into the equation for the dimensions of the rectangle.
The rectangle has one side measuring b yards and the adjacent side measuring a yards.
So the dimensions of the rectangle are b yards and (1/2b) yards.
Therefore, the pen that A'Lelia is building for her pet donkey is a rectangle with dimensions b yards and (1/2b) yards.
a. Write two different expressions giving the perimeter of the donkeys 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 donkeys pen.
a. The perimeter of a rectangle can be calculated by adding the lengths of all four sides. Therefore, the two different expressions giving the perimeter of the donkey's pen are:
Expression 1: 2b + 2(1/2b) = 2b + b = 3b
Expression 2: b + (1/2b) + b + (1/2b) = 2b + 2(1/2b) = 3b
B. Let's choose a value for a that is 10. This means that b = 2a = 2(10) = 20. Now, we will evaluate the perimeter of the pen using Expression 1:
Perimeter = 3b = 3(20) = 60 yards
C. I used Expression 1 to evaluate the perimeter of the donkey's pen because it simplifies the calculation by directly multiplying the length of one side, b, by 3, which is the sum of all four sides of the rectangle. This expression is more straightforward and less prone to calculation errors.