The perimeter of a triangle is 6p2
-4p+9 and two of its sides are p2
-2p+1 and 3p2
-5p+3.Find the third
side of the triangle

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Solution

$Let a, b and c be the 3 sides of the ∆ . Now, a = p^{2} - 2 p + 1 b = 3 p^{2} - 5 p + 3 c = ? Now, perimeter of ∆ = 6 p^{2} - 4 p + 9 \Rightarrow a + b + c = 6 p^{2} - 4 p + 9 \Rightarrow p^{2} - 2 p + 1 + 3 p^{2} - 5 p + 3 + c = 6 p^{2} - 4 p + 9 \Rightarrow 4 p^{2} - 7 p + 4 + c = 6 p^{2} - 4 p + 9 \Rightarrow c = 6 p^{2} - 4 p + 9 - 4 p^{2} + 7 p - 4 \Rightarrow c = 2 p^{2} + 3 p + 5 So, third side of the triangle = 2 p^{2} + 3 p + 5$

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Q. The perimeter of a triangle is

6 p^{2} - 4 p + 9

and two of its sides are

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and

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. Find the third side of the triangle.

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