Question

The sides of a triangle are 7 cm, 9 cm and 14 cm. Its area is

Options

• \[12\sqrt{5} c m^2\]

   

• \[12\sqrt{3} c m^2\]

   

• \[24\sqrt{5} c m^2\]

   

• \[63 c m^2\]

   

Answer 1

The area of a triangle having sides a, b, c and s as semi-perimeter is given by,

`A = sqrt(s(s-a)(s-b)(s-c))` , where

`s = (a+b+c)/2`

Therefore the area of a triangle having sides 7 cm, 9 cm and 14 cm is given by

a = 7 cm ; b = 9 cm ; c = 14 cm

`s = (a+b+c)/2`

`s = (7+9+14)/2`

`s = 30/2`

s = 15 cm 

`A = sqrt(15(15-7)(15-9)(15-14))`

`A = sqrt(15(8)(6)(1))`

`A = sqrt(720)`

`A = 12 sqrt(5)  cm^2`