Question

In the diagram below of triangle J, K, LJKL, MM is the midpoint of start overline, J, L, end overline

JL
and NN is the midpoint of start overline, K, L, end overline
KL
. If M, N, equals, 40, minus, 5, xMN=40−5x, and J, K, equals, 4, x, minus, 18JK=4x−18, what is the measure of start overline, J, K, end overline
JK
?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Given that MM is the midpoint of JL and NN is the midpoint of KL, we know that MJ = ML and KN = NL.

Since MN = 40 - 5x, we can set up an equation:
MJ + KN = MN
ML + NL = 40 - 5x
2MJ + 2KN = 40 - 5x
2(MJ + KN) = 40 - 5x
2(JK) = 40 - 5x
JK = 20 - 2.5x
Now we also know that JK = 4x - 18
So, 4x - 18 = 20 - 2.5x
6.5x = 38
x = 38 / 6.5
x = 5.846
Therefore, the measure of JK is:
JK = 4(5.846) - 18
JK = 23.384 - 18
JK = 5.384.