Solution:
Given:
Perimeter of triangular piece of land (P) = 1800m
Ratio of the length of triangular sides (a:b:c) = 5:6:7
To find: Area of the triangular piece of land (A)
Let, the common unit for the length of sides be x.
The, a = 5x, b = 6x and c = 7x
We know that,
Perimeter of a triangle (P) = a + b + c
Or, 1800 m = 5x + 6x + 7x
Or, 18x = 1800 m
Or, x = 100 m
∴ a = 5x = 5*100 m = 500 m
b = 6x = 6*100 m = 600 m
c = 7x = 7*100 m = 700 m
Again,
Semi-peremeter (s) = half of the perimeter = \(\frac P2\)
= \(\frac{100}2\)
= 900 m
Now, by formula,
Area of triangle (A) = \(\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\)
= \(\sqrt{900\left(900-500\right)\left(900-600\right)\left(900-700\right)}\)
= \(\sqrt{21600000000m^4}\)
= \(\sqrt{\left(146969.38m^2\right)^2}\)
= 146969.38 m2
Hence the area of triangular piece of land is 146969.38 m2 is the required answer