Question

I’m just confused and don’t know how to solve this

Answer 1

MK = 22 units

1) Examining that triangle, we can notice that the line segment EF divides into two halves the legs LM and LK.

2) And since LF ≅ FM and LE ≅ EK then we can state that FE is the Midsegment of that triangle. Therefore we can write out the following ratio:

`\begin{gathered} M=(1)/(2)\cdot b \\ 35+2x=(1)/(2)\cdot(x+34) \\ 35+2x=(x)/(2)+17 \\ 2x=(1)/(2)x-18 \\ (3)/(2)x=-18 \\ 3x=-36 \\ x=-12 \end{gathered}`

Now that we have the quantity of x, let's plug it into the length of MK, given by the formula x+34

`\begin{gathered} MK=x+34 \\ MK=-12+34 \\ MK=22 \end{gathered}`

Hence, the length of MK is 22 units