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Question
The sides of a triangle are 7 cm, 9 cm and 14 cm. Its area is
Options
- \[12\sqrt{5} c m^2\]
- \[12\sqrt{3} c m^2\]
- \[24\sqrt{5} c m^2\]
- \[63 c m^2\]
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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 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`
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