Answer:
Area = 587877.54 [tex]m^{2}[/tex]
Step-by-step explanation:
Let the length of sides of the triangle be represented by a, b and c respectively.
a = [tex]\frac{5}{18}[/tex] x 3600
= 1000
b = [tex]\frac{6}{18}[/tex] x 3600
= 1200
c = [tex]\frac{7}{18}[/tex] x 3600
= 1400
The length of the sides of the triangle are: 1000 m , 1200 m, 1400 m.
Perimeter = a + b + c
= 1000 + 1200 + 1400
= 3600
The area of the land can be determined by;
Area of a triangle = [tex]\sqrt{(s*(s-a)* (s-b)* (s-c))}[/tex]
where: s is the semi-perimeter of the triangle and a, b and c are the length of sides respectively.
s = [tex]\frac{perimeter}{2}[/tex]
= [tex]\frac{3600}{2}[/tex]
s = 1800
Area = [tex]\sqrt{(1800(1800 - 1000)*(1800 - 1200)*(1800 - 1400))}[/tex]
= [tex]\sqrt{(1800*800*600*400)}[/tex]
= [tex]\sqrt{345600000000}[/tex]
= 587877.54
Area = 587877.54 [tex]m^{2}[/tex]
The area of the triangle is 587877.54 [tex]m^{2}[/tex].
