Find the third side of a triangle whose two sides are $(3 x^{2} - 5 x)$ cm and $(4 x^{2} + 12)$ cm and perimeter is $(8 x^{2} - 9 x + 4)$ cm.

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Solution

Let the unknown side be $y$ cm.

Perimeter of the triangle = sum of its three sides

$⟹$ $8 x^{2} - 9 x + 4$ = $(3 x^{2} - 5 x)$ + $(4 x^{2} + 12)$ + $y$

$⟹ y = (8 x^{2} - 9 x + 4) - (3 x^{2} - 5 x) - (4 x^{2} + 12)$

$⟹ y = 8 x^{2} - 9 x + 4 - 3 x^{2} + 5 x - 4 x^{2} - 12$

$⟹ y = 8 x^{2} - 4 x^{2} - 3 x^{2} - 9 x + 5 x + 4 - 12$

$⟹ y = (x^{2} - 4 x - 8) c m$

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