Parallelogram PARL is similar to parallelogram WXYZ. If AP= 25, PL=29, and WZ= 145, Find the value of c.
We can set up a proportion:
$$\frac{WZ}{AP} = \frac{YZ}{PL+c}$$
Plugging in the given values, we get:
$$\frac{145}{25} = \frac{YZ}{29+c}$$
Simplifying, we get:
$$5.8 = \frac{YZ}{29+c}$$
Multiplying both sides by $29+c$:
$$5.8(29+c) = YZ$$
Expanding and simplifying:
$$168.2 + 5.8c = YZ$$
Since PARL is similar to WXYZ, we know that the corresponding sides are proportional. In particular, we know that:
$$\frac{AP}{WZ} = \frac{PL}{YZ}$$
Plugging in the given values and solving for $YZ$, we get:
$$\frac{25}{145} = \frac{29}{YZ} \implies YZ = \frac{145\cdot 29}{25} = 168.2$$
Comparing this to our earlier expression, we see that:
$$168.2 + 5.8c = YZ = 168.2$$
Thus, $c=\boxed{0}$.