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Mark the correct alternative in each of the following:

The sides of a triangle are 16 cm, 30 cm, 34 cm. Its area is

#### Options

225 cm

^{2}225 \[\sqrt{3}\] cm

^{2}225 \[\sqrt{2}\] cm

^{2}450 cm

^{2 }none above

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#### Solution

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 say *A, *having sides 16 cm, 30 cm and 34 cm is given by

*a* = 16 cm ; *b* = 30 cm ; *c* = 34 cm

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

`s = (16 + 30 +34 )/2`

`s = 80/2`

s = 40 cm

Therefore the area of the triangle is

`A = sqrt(40(40-16)(40-30)(40-34))`

`A = sqrt(40(24)(10)(6))`

`A = sqrt(57600)`

A = 240 cm^{2}

#### Notes

No option is correct

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