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Part 1
The perimeter of the parallelogram to the right is 88.8. The length of side JM overbar is 15. Find the lengths of KL overbar, JK overbar, and ML overbar.
To find the lengths of KL, JK, and ML, we can start by finding the length of side LK. Since a parallelogram has opposite sides that are equal in length, we have LK = JM = 15.
Next, we can use the fact that the perimeter of a parallelogram is the sum of all four sides. Let's denote the lengths of JK and ML as x and y, respectively. The perimeter formula can be written as:
88.8 = JM + JK + KL + ML
88.8 = 15 + x + 15 + y
88.8 = 30 + x + y
We also know that the opposite sides of a parallelogram are equal in length, so KL = JM = 15 and JK = ML.
Substitute these values into the equation above:
88.8 = 30 + 15 + 15
88.8 = 60 + x + x
88.8 = 60 + 2x
28.8 = 2x
x = 14.4
So, the length of JK is 14.4. Since JK = ML, the length of ML is also 14.4.
Finally, we can find the length of side KL:
KL = JM = 15
Therefore, the lengths of KL, JK, and ML are 15, 14.4, and 14.4, respectively.