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:

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

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