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.
Let's choose a = 8.
If the length is 2a, then the length would be 2(8) = 16.
If the width is a + 6, then the width would be 8 + 6 = 14.
The perimeter of the pen would be 2(length + width) = 2(16 + 14) = 2(30) = 60 units.
Explain why you used that expression to evaluate the perimeter of the
donkey’s pen.
The expression 2(length + width) is used to evaluate the perimeter of the donkey's pen because the perimeter is defined as the total distance around the boundary of a shape. In this case, the shape is a rectangle (the donkey's pen), so the perimeter is the sum of all four sides of the rectangle.
In the expression 2(length + width), we are doubling the sum of the length and width because a rectangle has two pairs of equal sides. By adding the length and width together, we get the total distance of one pair of opposite sides, and then by doubling that sum, we account for all four sides of the rectangle.
Therefore, by using the expression 2(length + width), we can accurately calculate the perimeter of the donkey's pen.
To find the perimeter of the pen, we first need to determine the length of each side.
Let's assume the length of one side of the pen is 'a'. Since you mentioned we need a value greater than 5 and less than 15, let's choose a value of 'a' as 10.
The perimeter of a pen, P, can be calculated by adding together the lengths of all sides.
Since a pen usually has 4 equal sides, we can use the formula P = 4a to find the perimeter.
Substituting the value of 'a' into the formula, we get:
P = 4 * 10 = 40.
So, the perimeter of the pen, when the length of one side is chosen as 10, is 40 units.