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Question
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 cm2
225 \[\sqrt{3}\] cm2
225 \[\sqrt{2}\] cm2
450 cm2
none above
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 cm2
Notes
No option is correct
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