If I, J, equals, 61IJ=61, J, K, equals, 80JK=80, and M, N, equals, 60MN=60, find the length of start overline, L, M, end overline
LM
. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
LM=
LM = MN + NIJ + JLM
Given:
IJ = 61
JK = 80
MN = 60
We can find NIJ and JLM using the Pythagorean Theorem.
NIJ = √(IJ^2 + JK^2)
= √(61^2 + 80^2)
= √(3721 + 6400)
= √10121
= 100.6 (rounded to the nearest tenth)
JLM = √(JK^2 + LM^2)
LM = √(JLM^2 - JK^2)
= √(80^2 - 61^2)
= √(6400 - 3721)
= √(2679)
≈ 51.8 (rounded to the nearest tenth)
Therefore, the length of LM is approximately 100.6 + 60 + 51.8 = 212.4 units.