Question

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?

Answer 1

Since LM is a midsegment, we get,

`LM\text{ = }(1)/(2)HK`
`71\text{ - 9x = }(1)/(2)(23\text{ - x)}`
`(71-9x)(2)\text{ = 23 - x}`
`142\text{ - 18x = 23 - x}`
`142\text{ - 23 = -x + 18x}`
`\text{ 119 = 17x}`
`(119)/(17)=(17x)/(17)`
`7\text{ = x }\rightarrow\text{ x = 7}`

Since we've determined that x = 7, let's find the value of LM by plugging in x = 7 in the equation.

`LM\text{ = 71 - 9x}`
`LM\text{ = 71 - 9}(7)`
`LM\text{ = 71 - 63}`
`LM\text{ = 8}`

Therefore, the measure of LM = 8.