Let the sides be 3x , 5x and 7x .
so which implies that
3x + 5x + 7x = 300
15x = 300
x = 300/15
x = 20 .
now the sides are 3x = 3*20 = 60 m
5x = 5*20 = 100 m
7x = 7*20 = 140 m
semi perimeter = 60 + 100 + 140 / 2
= 150 m
using herons' formula ;
area = root s (s-a) (s-b) (s-c)
= root 150 (150- 60) (150- 100) (150- 140)
= 150*90*50*10
= 1500 root 3 ( by prime factorisation )

Given:
The sides of a triangular plot are in the ratio 3:5:7.
The perimeter of the triangular plot is 300.

To find:
The area of the triangular plot.

Solution:

Step 1: Understanding the problem
We are given the sides of the triangular plot in the ratio 3:5:7. Let's assume the three sides are 3x, 5x, and 7x, where x is the common ratio.
The perimeter of the triangular plot is given as 300. Therefore, we can write the equation as:
3x + 5x + 7x = 300

Step 2: Solving the equation
Combining like terms, we get:
15x = 300

Dividing both sides by 15, we obtain:
x = 20

Step 3: Finding the lengths of the sides
Now that we know the value of x, we can find the lengths of the sides by substituting x = 20 into the sides' ratios:
Side 1: 3x = 3 * 20 = 60
Side 2: 5x = 5 * 20 = 100
Side 3: 7x = 7 * 20 = 140

Step 4: Calculating the area of the triangular plot
To find the area of the triangular plot, we can make use of Heron's formula, which states that the area of a triangle with sides a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle.

Calculating the semi-perimeter (s):
s = (a + b + c) / 2
= (60 + 100 + 140) / 2
= 300 / 2
= 150

Now, substituting the values into the formula:
Area = √(150(150-60)(150-100)(150-140))
= √(150 * 90 * 50 * 10)
= √67500000
= 8229.128

Step 5: Final answer
The area of the triangular plot is approximately 8229.128 square units.

Summary:
The triangular plot has sides measuring 60 units, 100 units, and 140 units. By using Heron's formula, we calculated the area of the triangular plot to be approximately 8229.128 square units.