Question

Find the area, if the side of a triangle is in the ratio 2:3:4 and the perimeter of the triangle is 108. (Heron's formula)​

Answer 1

Answer:

Step-by-step explanation:

let the common factor be x

so sides are 2x, 3x, 4x

p = 108 units

2x+3x+4x = 108 units

9x = 108 units

x = 12 units

sides are 24 units, 36 units, 48 units

AREA BY HERON'S FORMULA

semi p = 24+36+48/2

           = 54 units

A = $\sqrt{54(54-24)(54-36)(54-48)}$

   = $\sqrt{54*30*18*6}$

    = $\sqrt{174960}$

    =418.28 unit²

Answer 2

The best known and the simplest formula, which almost everybody remembers from school is: area = 0.5 * b * h, where b is the length of the base of the triangle, and h is the height/altitude of the triangle. However, sometimes it's hard to find the height of the triangle.

let the common factor be x

so sides are 2x, 3x, 4x

p = 108 units

2x+3x+4x = 108 units

9x = 108 units

x = 12 units

sides are 24 units, 36 units, 48 units

AREA BY HERON'S FORMULA

semi p = 24+36+48/2

          = 54 units

A =  

  =  

   =  

   =418.28 unit²