Question 4
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 = 1/3 b.
a. Write two different expressions giving the perimeter of the donkey’s pen
Expression 1: Since the pen is a rectangle, the perimeter is equal to the sum of all four sides.
Therefore, the perimeter can be expressed as: P = a + b + a + b = 2a + 2b.
Expression 2: Given that a = 1/3 b, we can substitute this expression for a in the first expression of the perimeter.
P = (2 * (1/3 b)) + 2b = (2/3 b) + 2b = (2/3 + 1) b = (5/3) b.
Question 4
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.
a. The two different expressions giving the perimeter of the donkey's pen are:
1) P = 2a + 2b
2) P = (5/3) b
b. Let's choose a value of a = 8 yards.
Substituting this value in the first expression:
P = 2(8) + 2b = 16 + 2b
To evaluate the perimeter, we need to know the value of b. Let's assume b = 10 yards.
P = 16 + 2(10) = 16 + 20 = 36 yards.
Therefore, for a = 8 yards and b = 10 yards, the perimeter of the donkey's pen is 36 yards.
i want 7
Sure, let's evaluate the perimeter using the second expression for a value of a = 7 yards.
The second expression is P = (5/3) b.
Let's assume b = 10 yards.
P = (5/3) * 10
P = 50/3
P ≈ 16.67 yards (rounded to two decimal places).
Therefore, for a = 7 yards and b = 10 yards, the perimeter of the donkey's pen is approximately 16.67 yards.
i mean 9
Apologies for the confusion. Let's evaluate the perimeter using the second expression for a value of a = 9 yards.
The second expression is P = (5/3) b.
Let's assume b = 10 yards.
P = (5/3) * 10
P = 50/3
P ≈ 16.67 yards (rounded to two decimal places).
Therefore, for a = 9 yards and b = 10 yards, the perimeter of the donkey's pen is approximately 16.67 yards.
c. Explain why you used that expression to evaluate the perimeter of the
donkey’s pen
In this case, I used the second expression, P = (5/3) b, to evaluate the perimeter of the donkey's pen because it was derived from the given information that a = 1/3 b.
By substituting this value of a into the first expression for the perimeter (P = 2a + 2b), we obtained the second expression (P = (5/3) b).
Since we know the value of a, which is 9 yards, we can use the second expression to calculate the perimeter by substituting the value of b, which we assumed to be 10 yards in this case. This allows us to obtain the perimeter value of approximately 16.67 yards.