The perimeter of a parallelogram is calculated by the formula:
Perimeter = 2(AB + AD)
In this case, we are given that the perimeter is 46 inches. Therefore, we can set up the equation:
2(AB + AD) = 46
To simplify, we divide both sides by 2:
AB + AD = 23
Next, we need to remember that in a parallelogram, opposite sides are equal. This means:
AB = CD
AD = BC
Since we have two pairs of equal sides, we can express the relationship between the lengths of these sides. If we denote the length of side AB as x and the length of side AD as y, the equation becomes:
x + y = 23
Without additional information about the length of side AB (or any other side), we cannot definitively find the length of side DA (AD). However, we understand that the relationship between both sides must always hold true. For example, if AB is 10 inches, then:
10 + AD = 23
This would lead to:
AD = 23 – 10 = 13 inches
Thus, the length of side DA (AD) depends on the measurement of side AB. In summary, if you have the length of any one side of the parallelogram, you can easily find the length of DA using:
DA = 23 – AB
Without the specific value for side AB, we can only describe the relationship between the sides rather than give an exact measurement for DA.