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The perimeter of a triangle is (15x2- 23x + 9) and two of its sides are (5x2 + 8x -1) and 6x2 - 9x + 4. Find the third side.
1. 4x2 + 22x +6
2. 4x2 - 22x + 6
3. 3x2 - 22x +6
4. 3x2 - 21x + 6

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Correct Answer - Option 2 : 4x2 - 22x + 6

Given

The perimeter of a triangle is (15x2- 23x + 9)

Two of its sides are (5x2 + 8x -1) and (6x2 - 9x + 4)

Concept

Perimeter of a triangle = Sum of the lengths of its three sides.

Calculation

⇒ 15x2- 23x + 9 = (5x2 + 8x -1) + (6x2 - 9x + 4) + third side 

⇒ 15x2- 23x + 9 = (11x2 - x + 3) + third side 

⇒ The third side = (15x2- 23x + 9) - (11x2 - x + 3)

⇒ The third side = 4x2 - 22x + 6

∴ The third side = 4x2 - 22x + 6

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