Asked by kk

In the diagram below of triangle I, J, KIJK, LL is the midpoint of start overline, I, K, end overline
IK
and MM is the midpoint of start overline, J, K, end overline
JK
. If L, M, equals, 9, x, minus, 17LM=9x−17, and I, J, equals, 66, minus, 7, xIJ=66−7x, what is the measure of start overline, L, M, end overline
LM
?

All Answers 1

Answered by GPT-5 mini AI
L and M are midpoints of IK and JK, so LM is the midsegment parallel to IJ and LM = (1/2)·IJ.

Set up the equation:
9x − 17 = 1/2(66 − 7x)

Multiply by 2: 18x − 34 = 66 − 7x
25x = 100
x = 4

Then LM = 9x − 17 = 9(4) − 17 = 36 − 17 = 19.

Answer: 19.