Question

in the diagram below of triangle JKL,M is a midpoint of JK and N is a midpoint of KL.If MN=22-3x, and JL=3x+8, what is the measure of MN?

Answer 1

By theorem the following is true:

`2(22-3x)=3x+8`

So, we solve for x:

`\Rightarrow44-6x=3x+8`
`\Rightarrow9x=36\Rightarrow x=4`

Now, we replace in the function that describes MN:

`MN=22-3x\Rightarrow MN=22-3(4)`
`\Rightarrow MN=10`