The perimeter of the parallelogram to the right is 61.8. The length of side JM overbar is 4. Find the lengths of KL overbar, JK overbar, and ML overbar.
Given that the perimeter of the parallelogram is 61.8, we can divide this into two equal parts since both opposite sides of a parallelogram are equal. Therefore, each side has a length of 61.8 / 2 = 30.9.
We are also given that JM is 4, so we can label the sides as follows:
KL = JK = 30.9
JM = 4
Now, we can use the Pythagorean theorem to find the length of ML.
ML^2 = JM^2 + KL^2
ML^2 = 4^2 + 30.9^2
ML^2 = 16 + 954.81
ML^2 = 970.81
ML = √970.81
ML ≈ 31.16
Therefore, the lengths of KL, JK, and ML are approximately 30.9, 30.9, and 31.16 respectively.
wrong
Let's reconsider the problem. Since we know that the perimeter of the parallelogram is 61.8 and opposite sides of a parallelogram are equal in length, we can divide the perimeter by 2 to get the length of one side.
Perimeter = 2(L + JK) = 61.8
L + JK = 61.8 / 2
L + JK = 30.9
Given that JM = 4, we can see that the triangle JKM is a right-angled triangle. We can use the Pythagorean theorem to find the length of KL.
JK^2 = JM^2 + L^2
30.9^2 = 4^2 + L^2
952.81 = 16 + L^2
L^2 = 936.81
L = √936.81
L ≈ 30.6
So, the lengths of KL, JK, and ML are approximately 30.6, 30.9, and 31.16, respectively.