Let the breadth of the land be denoted as $b$, and the length as $l$.

We are told that the length is 15% more than the breadth, which can be written as:

$l = 1.15b$

The area of the rectangle (land) is given as 460 cm². The formula for the area of a rectangle is:

$\text{Area} = l \times b$

Substituting $l = 1.15b$ into this formula:

$460 = 1.15b \times b$

Simplifying:

$460 = 1.15b^2$

To solve for $b$, divide both sides of the equation by 1.15:

$b^2 = \frac{460}{1.15}$ $b^2 = 400$ $b = \sqrt{400} = 20$

So, the breadth $b$ is 20 cm.

Now, using $l = 1.15b$, we can find the length:

$l = 1.15 \times 20 = 23 \, \text{cm}$

The perimeter of a rectangle is given by the formula:

$\text{Perimeter} = 2(l + b)$

Substituting the values for $l$ and $b$:

$\text{Perimeter} = 2(23 + 20) = 2 \times 43 = 86 \, \text{cm}$

Therefore, the perimeter of the land is 86 cm.

Would you like more details on how this was calculated, or have any questions?

Here are some related questions for you:

1. How would the perimeter change if the length were 25% more than the breadth?
2. What is the area of a rectangle if the length is 30 cm and the breadth is 15 cm?
3. How do you find the area and perimeter of a triangle?
4. What would happen if the breadth was decreased by 10%?
5. Can the same formula for area and perimeter apply to a circle?

Tip: When solving problems like this, always express relationships clearly first (like "15% more than") before applying the area formula.