Question

The perimeter of a scalene triangle is 29a + 9b - 6c.Two of its sides are 16a + 5b - 2c and -6a + 7b - 12c .Find the third side.


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Answer 1

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Answer 2

$\bigstar$ Question :

$\mapsto$ The perimeter of a scalene triangle is 29a + 9b - 6c.Two of its sides are 16a + 5b - 2c and -6a + 7b - 12c .Find the third side.

$\bigstar$ To Find :

$\mapsto$ Third side of the scalene triangle =?

$\bigstar$ Given :

$\mapsto$ 1st side of triangle = 16a+5b-2c

$\mapsto$ 2nd side of triangle = -6a+7b-12c

$\mapsto$ Perimeter of scalene triangle = 29a+9b-6c.

$\bigstar$ Required Formula :

$\mapsto$ Perimeter of scalene triangle = a+b+c

$\bigstar$ Solution :

We know that,

• Perimeter of triangle is equal to its sum of three unequal sides.

So,Let us consider that

• 1st side of triangle be a ,
• 2nd side of triangle be b,
• and 3rd side of triangle be c.

Putting values,

☛ 29a+9b-6c = (16a+5b-2c) + (-6a+7b-12c) + c

☛ 29a+9b-6c = 16a + 5b - 2c - 6a + 7b - 12c + c

☛ 29a+9b-6c = 10a + 12b - 14c + c

☛ C = 10a+12b-14c - 29a+9b-6c

☛ C = -19a + 21b - 20c

$\therefore$ The Third side of triangle = c = -19a + 21b - 20c.

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