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in the diagram below of triangle HJK,L is a midpoint of HJ and M is a midpoint of JK. If LM=71-9x, and HK=23-x , what is the measure of LM?

in the diagram below of triangle HJK L is a midpoint of HJ and M is a midpoint of JK If LM 71 9x and

Answer :

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.

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