Question

In the diagram below of the triangle H J K, L is a midpoint of HJ, and M is a midpoint of JK. If LM = 71 - 9x and HK = 23 - x, what is the measurement of LM?

Answer 1

The measurement of LM is (23 - x)/2.

Explanation:

We are given that L is a midpoint of HJ, and M is a midpoint of JK.

This means that HL = LJ and JM = MK. We are also given that LM = 71 - 9x and HK = 23 - x. We need to find the value of LM.

Since L is the midpoint of HJ, we can write:

HL = LJ = HK/2

Since M is the midpoint of JK, we can write:

JM = MK = HK/2

Therefore, we can write:

LM = HL + JM = HK/2 + HK/2 = HK

Now we can substitute HK = 23 - x into the expression for LM:

LM = (23 - x)/2

Therefore, the measurement of LM is (23 - x)/2.