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Addition and Subtraction of Algebraic Expression

The perimeter...

Question

The perimeter of a triangle is $8 + 13 a + 7 a^{2}$ and two of its sides are $2 a^{2} + 3 a + 2$ and $3 a^{2} - 4 a - 1$ . Find the third side of the triangle.

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Solution

Two sides of triangle are $2 a^{2} + 3 a + 2$ and $3 a^{2} - 4 a - 1$
Let the third side be $s$
Perimeter $= 8 + 13 a + 7 a^{2} =$ $2 a^{2} + 3 a + 2$ $+ 3 a^{2} - 4 a - 1 + s$
$⟹ s = 2 a^{2} + 15 a + 7$
So, the third side of triangle is $= 2 a^{2} + 15 a + 7$

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