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प्रश्न
Find the area of a triangle whose sides are 3 cm, 4 cm and 5 cm respectively.
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उत्तर
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 having sides 3 cm, 4 cm and 5 cm is given by
a = 3 cm ; b = 4 cm ; c = 5 cm
`s = (a+b+c)/2`
`s = (3+4+5)/2`
`s =12/2`
s = 6 cm Now, area `A = sqrt(s(s-a)(s-b)(s-c)`
\[= \sqrt{6(6 - 3)(6 - 4)(6 - 5)}\]
\[ = \sqrt{6 \times 3 \times 2 \times 1}\]
\[ = \sqrt{36}\]
\[ = 6 c m^2\]
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