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=1/3b
a. Write two different expressions giving the perimeter of the donkey’s pen.
The perimeter of a rectangle is given by the formula P = 2l + 2w, where l represents the length of the rectangle and w represents the width.
In this case, one side of the rectangle measures B yards, so the length (l) of the rectangle is B yards.
The other side of the rectangle measures A yards, and it is given that A = (1/3)B.
Therefore, the width (w) of the rectangle is (1/3)B yards.
Expression 1: P = 2(B) + 2((1/3)B)
Expression 2: P = 2(B/3) + 2(B)
can you explain more? i still don't get it
Certainly! Let's break it down step by step.
We're given that one side of the rectangle measures B yards, so we can label that side as the length (l) of the rectangle.
The other side of the rectangle measures A yards. And we're also given that A = (1/3)B, which means A is equal to one-third of B. We can label this side as the width (w) of the rectangle.
Now, to find the perimeter of the rectangle, we use the formula P = 2l + 2w.
Expression 1:
For the length (l), we know that it is B yards.
For the width (w), we know that it is (1/3)B yards.
So, substituting these values into the formula, we get:
P = 2(B) + 2((1/3)B)
Simplifying the expression gives us:
P = 2B + (2/3)B
Expression 2:
Again, for the length (l), we know that it is B yards.
And for the width (w), we know that it is (1/3)B yards.
So, substituting these values into the formula, we get:
P = 2(B/3) + 2(B)
Simplifying the expression gives us:
P = (2/3)B + 2B
These are two different expressions giving the perimeter of the donkey's pen. They are equal to each other and can be simplified further if needed.
i still dont get it
I apologize for any confusion. Let's try a different approach.
The perimeter of a rectangle is the sum of all the sides of the rectangle. In this case, the donkey's pen is a rectangle with one side measuring B yards and the adjacent side measuring A yards.
Since we know that A = (1/3)B, we can substitute this value of A into the formula for the perimeter.
Expression 1: P = 2(A + B)
We can replace A with (1/3)B in the expression:
P = 2((1/3)B + B)
Simplifying further:
P = 2(4/3)B
P = (8/3)B
Expression 2: P = 2B + 2A
We can replace A with (1/3)B in the expression:
P = 2B + 2((1/3)B)
Combining like terms:
P = 2B + (2/3)B
P = (6/3)B + (2/3)B
P = (8/3)B
So, both expressions give us the perimeter of the donkey's pen as (8/3)B. This means the perimeter is 8/3 times the length of one side B.
how did you do this:
P = 2(4/3)B
P = (8/3)B
and this:
P = 2B + (2/3)B
P = (6/3)B + (2/3)B
P = (8/3)B
I apologize for the incorrect simplifications in my previous response. Let's rectify the mistake.
Expression 1:
P = 2((1/3)B + B)
To simplify and find a common denominator, we multiply (1/3) by 3/3:
P = 2((1/3)B + (3/3)B)
Simplifying the expression within the parentheses:
P = 2((1/3)B + (3/3)B)
P = 2((1/3 + 3/3)B)
P = 2((4/3)B)
To distribute the 2 to the expression within the parentheses:
P = 2 * (4/3) * B
Multiplying 2 and 4/3 gives:
P = (8/3)B
Expression 2:
P = 2B + 2((1/3)B)
To simplify and find a common denominator, we multiply (1/3)B by 3/3:
P = 2B + 2((1/3)B * (3/3))
Multiplying (1/3)B and 3/3 gives:
P = 2B + 2((3/9)B)
Simplifying further:
P = 2B + (6/9)B
To find a common denominator between 2 and 6/9, we rewrite 2 as 18/9:
P = (18/9)B + (6/9)B
Combining like terms:
P = (18/9 + 6/9)B
P = (24/9)B
Simplifying 24/9 gives:
P = (8/3)B
So, the correct expressions for the perimeter of the donkey's pen are:
Expression 1: P = (8/3)B
Expression 2: P = (8/3)B
Both expressions give us the same result, which means the perimeter is (8/3) times the length of one side B. I apologize for the confusion caused by my previous incorrect simplifications.