Question

The difference between the semi-perimeter and the sides of a triangle are 16 cm, 14 cm and 10 cm respectively. Find the semi-perimeter of the triangle

Answer 1

Answer:

something is wrong here else if you find answer tell me also

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• The difference between the semi-perimeter and the sides of a triangle are 16 cm, 14 cm and 10 cm

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• Semi perimeter = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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let the semi perimeter be x

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let the sides of triangle be a , b , c

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Acc. to the question :-

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x - a = 16 --- ( i )

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x - b = 14 --- ( ii )

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x - c = 10 --- ( iii )

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• Now in eq ( i )

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x - a = 16

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x = 16 + a

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a = x - 16

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• Now in eq ( ii )

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x - b = 14

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x = 14 + b

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b = x - 14

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• Now in eq ( iii )

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x - c = 10

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x = 10 + c

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c = 10 - x

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We know that ;

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$\sf{\red{\boxed{\bold{Semi\: Perimeter = \dfrac{ a + b + c }{2}}}}}$

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Where ;

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a , b , c are the sides of triangle

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• Putting values in the formulae

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$\sf :\implies{\bold{ x = \dfrac{x - 16 + x - 14 + x - 10 }{2} }}$

$\sf :\implies{\bold{ x = \dfrac{x + x + x - 16 - 14 - 10 }{2} }}$

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$\sf :\implies{\bold{ x = \dfrac{3x - 40 }{2} }}$

$\sf :\implies{\bold{2x = 3x - 40 }}$

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$\sf :\implies{\bold{ -3x + 2x= - 40 }}$

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$\sf :\implies{\bold{ -x = - 40}}$

$\sf :\implies{\bold{ x = 40 }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Required semi perimeter = 40 cm