Solution :
Let's assume,
- side a = 3x
- side b = 4x
- side c = 5x
We know that perimeter of triangle is sum of all the sides.
a + b + c = Perimeter
3x + 4x + 5x = 84
12x = 84
x = 84/12
x = 7
Hence,
- side a = 3x = 3(7) = 21 cm
- side b = 4x =4(7) = 28 cm
- side c = 5x = 5(7) = 35 cm
Now,
Semi-perimeter = Perimeter/2
= 84/2
= 42 cm
Using heron's formula,
- Area = s√s - a)(s -b)(s -c)
Where,
- s is semi-perimeter
- a, b and c are sides of triangle.
= √42(42- 21)(42 ; 28)(42- 35)
= √42( 21 × 14 × 7)
= √42 × 2058
= √ 86,436
= 294 cm²
Therefore, Area of the triangle is 294 cm²