Since LM is a midsegment, we get,
[tex]LM\text{ = }\frac{1}{2}HK[/tex][tex]71\text{ - 9x = }\frac{1}{2}(23\text{ - x)}[/tex][tex](71-9x)(2)\text{ = 23 - x}[/tex][tex]142\text{ - 18x = 23 - x}[/tex][tex]142\text{ - 23 = -x + 18x}[/tex][tex]\text{ 119 = 17x}[/tex][tex]\frac{119}{17}=\frac{17x}{17}[/tex][tex]7\text{ = x }\rightarrow\text{ x = 7}[/tex]
Since we've determined that x = 7, let's find the value of LM by plugging in x = 7 in the equation.
[tex]LM\text{ = 71 - 9x}[/tex][tex]LM\text{ = 71 - 9}(7)[/tex][tex]LM\text{ = 71 - 63}[/tex][tex]LM\text{ = 8}[/tex]
Therefore, the measure of LM = 8.
