The garden is rectangular with its width 6 metres less than the length and the area of the land is 27m³. Determine a) Dimensions of the land, b) The total distance to be fenced.

Let $L$ be the length of the garden and $W$ be the width.
From the problem, the width is 6 meters less than the length:

The area of the rectangular garden is 27 m$^2$:

We can factor the quadratic equation:

This gives two possible values for $L$:

Since length cannot be negative, we take $L = 9$ meters.

Using the relationship $W = L - 6$:

The dimensions of the land are 9 meters by 3 meters.
The dimensions of the land are: Length = $\boxed{9 \text{ m}}$, Width = $\boxed{3 \text{ m}}$.

The formula for the perimeter $P$ of a rectangle is $P = 2(L + W)$.

The total distance to be fenced is $\boxed{24 \text{ m}}$.

The cost for 10 meters of fence is 10,000.
Cost per meter $= \frac{10,000}{10 \text{ m}} = 1,000 \text{ per meter}$

Total cost $= \text{Total distance} \times \text{Cost per meter}$
Total cost $= 24 \text{ m} \times 1,000 \text{ per meter}$
Total cost $= 24,000$
The total cost of fencing is $\boxed{24,000}$.