Correct Answer - Option 2 : 432√5 cm
2
Given:
The ratio of the side of a triangle = 8 ∶ 7 ∶ 9
The perimeter of triangle = 144
Formula required:
The perimeter of triangle = sum of the sides of the triangle
Area of a triangle =\(√ {s(s - a)(s - b)(s - c)}\)
S = (a + b + c)/2
Where a,b, c are the sides of a triangle
Calculations:
S = (8x + 7x + 9x)/2
a + b + c = 144
S = 144/2
⇒ 72
24x = 144
⇒ x = 6
Hence, a = 8 × 6
⇒ 48cm
b = 7 × 6
⇒ 42cm
c = 9 × 6
⇒ 54cm
Area of a triangle = \(√{72(72 - 48)(72 - 42)(72 - 54)}\)
⇒ 432√5 cm2
