Question

The sides of a triangular field are in the ratio of 5:6: 7. If its perimeter is 3600 m. find the area of that land

Answer 1

Answer:

Area = 587877.54 $m^{2}$

Step-by-step explanation:

Let the length of sides of the triangle be represented by a, b and c respectively.

a = $\frac{5}{18}$ x 3600

  = 1000

b = $\frac{6}{18}$ x 3600

  = 1200

c = $\frac{7}{18}$ 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 =  $\sqrt{(s*(s-a)* (s-b)* (s-c))}$

where: s is the semi-perimeter of the triangle and a, b and c are the length of sides respectively.

s = $\frac{perimeter}{2}$

 = $\frac{3600}{2}$

s = 1800

Area = $\sqrt{(1800(1800 - 1000)*(1800 - 1200)*(1800 - 1400))}$

        = $\sqrt{(1800*800*600*400)}$

        = $\sqrt{345600000000}$

        = 587877.54

Area = 587877.54 $m^{2}$

The area of the triangle is 587877.54 $m^{2}$.