Question

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, 8, x, minus, 53LM=8x−53, and I, J, equals, minus, 26, plus, 6, xIJ=−26+6x, what is the measure of start overline, L, M, end overline
LM
?

Answer 1

Since LL is the midpoint of start overline, I, K, end overline IK, we know that LL = 1/2(IK). Similarly, MM is the midpoint of start overline, J, K, end overline JK, so MM = 1/2(JK).

We are given that LM = 8x - 53 and IJ = -26 + 6x.

Since LL = 1/2(IK), we have LL = 1/2(IK) = 1/2(IJ + JK) = 1/2(IJ + MM), then

8x - 53 = 1/2(-26 + 6x + MM).

We know that MM = 1/2(JK), so MM = 1/2(IJ + JK). Since IJ = -26 + 6x, then JK = MM = 1/2(IJ) = 1/2(-26 + 6x) = -13 + 3x.

Substitute this into the equation above:

8x - 53 = 1/2(-26 + 6x + (-13 + 3x))

8x - 53 = 1/2(-39 + 9x)

16x - 106 = -39 + 9x

7x = 67

x = 67/7 = 9.57

So, the measure of LM is LM = 8(9.57) - 53 = 20.56.