Form an equation that relates x, y, z with the total area of the garden. Hence solve the system of simultaneous equations to find the areas x, y and z of the three plots.

The total area of the garden is given as 2 square units.
So, the equation is:

$$x + y + z = 2$$

We are given $\frac{x+2y}{3} = \frac{y+2z}{4} = \frac{2x+z}{5} = k$. This gives us:

1. $x+2y = 3k$
2. $y+2z = 4k$
3. $2x+z = 5k$ And from Step 1:
4. $x+y+z = 2$

From (1), $x = 3k - 2y$.
From (3), $z = 5k - 2x$. Substitute $x$:
$z = 5k - 2(3k - 2y) = 5k - 6k + 4y = -k + 4y$.
Now substitute $z$ into (2):
$y + 2(-k + 4y) = 4k$
$y - 2k + 8y = 4k$
$9y = 6k \implies y = \frac{6k}{9} = \frac{2k}{3}$.

Now find $x$ and $z$ using $y = \frac{2k}{3}$:
$x = 3k - 2\left(\frac{2k}{3}\right) = 3k - \frac{4k}{3} = \frac{9k - 4k}{3} = \frac{5k}{3}$.
$z = -k + 4\left(\frac{2k}{3}\right) = -k + \frac{8k}{3} = \frac{-3k + 8k}{3} = \frac{5k}{3}$.

$$\frac{5k}{3} + \frac{2k}{3} + \frac{5k}{3} = 2$$ $$\frac{12k}{3} = 2$$ $$4k = 2$$ $$k = \frac{1}{2}$$

$x = \frac{5}{3} \left(\frac{1}{2}\right) = \frac{5}{6}$
$y = \frac{2}{3} \left(\frac{1}{2}\right) = \frac{1}{3}$
$z = \frac{5}{3} \left(\frac{1}{2}\right) = \frac{5}{6}$

The areas are $\boxed{x = \frac{5}{6} square units, y = \frac{1}{3} square units, z = \