#### Answer

$MK = 16.5$

#### Work Step by Step

In similar triangles, corresponding sides are proportional. In order for us to find $MK$, we want to locate two corresponding sides that actually have values already to find out what the scale factor is. The scale factor for all corresponding sides is the same.
We are given the values of the corresponding sides $DF$ and $HK$, so let's set up that ratio to find the scale factor:
$\frac{DF}{HK} = \frac{30}{18}$
Divide both the numerator and denominator by their greatest common factor, $6$:
$\frac{DF}{HK} = \frac{5}{3}$
Now, let's set up the proportion for the corresponding sides $GF$ and $MK$ using the scale factor:
$\frac{27.5}{MK} = \frac{5}{3}$
Cross multiply:
$5(MK) = 82.5$
Divide both sides by $5$ to solve for $MK$:
$MK = 16.5$