The length of a rectangular plot is thrice its breadth. The area of the plot is $768{\text{m}}^2$. Find the perimeter of the plot.

Let the breadth of the rectangular plot be $b$ meters.
Then, the length of the plot $l=3b$ meters.

We know the formula for the area of a rectangle:

$$\text{Area}=\text{Length}\times \text{Breadth}$$

$$768=3b\times b$$

$$3b^2=768$$

$$b^2=\frac{768}{3}=256$$

$$b=\sqrt{256}=16\text{m}$$

Now find the length:

$$l=3b=3\times 16=48\text{m}$$

The formula for the perimeter of a rectangle is:

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

$$\text{Perimeter}=2(48+16)=2\times 64=128\text{m}$$