SOLUTION: A triangular park has sides 120 m,50 m and 80 m. Find the area of triangular park. A wire is rotated around the park leaving 3 m area. If cost of 1 m wire is 20 rs, then find the c

Algebra ->  Surface-area -> SOLUTION: A triangular park has sides 120 m,50 m and 80 m. Find the area of triangular park. A wire is rotated around the park leaving 3 m area. If cost of 1 m wire is 20 rs, then find the c      Log On


   

Question 985340: A triangular park has sides 120 m,50 m and 80 m. Find the area of triangular park. A wire is rotated around the park leaving 3 m area. If cost of 1 m wire is 20 rs, then find the cost of total wire to be used.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!

I will answer only the first part of the question regarding the area of the park (the area of the given triangle).

Use the Heron's formula for the triangle area:

S = sqrt%28p%28p-a%29%28p-b%29%28p-c%29%29.

named after the ancient Greek mathematician Heron.
Here  a,  b  and  c  are the measures of a triangle sides and  p  is half of the perimeter:  p = %28a+%2B+b+%2B+c%29%2F2.

In our case a = 120 m, b= 50 m, and c = 80 m. Hence, the semi-perimeter is

p = %28120+%2B+50+%2B+80%29%2F2 = 250%2F2 = 125 m

and the area of the given triangle is

S = sqrt%28125%2A%28125-120%29%2A%28125-50%29%2A%28125-80%29%29 = sqrt%28125%2A5%2A75%2A45%29 = sqrt%285%5E7%2A3%5E3%29 = 5%5E3.3.sqrt%2815%29 = 375.sqrt%2815%29 = 1452.37 m%5E2 (approximately).

For the Heron's formula see the lessons
    - Formulas for area of a triangle,
    - Proof of the Heron's formula for the area of a triangle  and
    - One more proof of the Heron's formula for the area of a triangle
in this site.