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

$m^{2} - 4 m - 8$

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$m^{2} + 4 m - 8$

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$m^{2} - 4 m + 8$

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$m^{2} + 4 m + 8$

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Solution

The correct option is A
$m^{2} - 4 m - 8$

Let the unknown side be $x$ .

Perimeter of the triangle = sum of its three sides

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

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

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

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

$⟹$ $x$ = $m^{2} - 4 m - 8$

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Similar questions

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

8 m^{2} - 9 m + 4

3 m^{2} - 5 m

4 m^{2} + 12

9 m^{2} - 2 n + 8

4 m^{2} + 3 n

7 m^{2} + 5 n - 12

Factorise : m^{4} - 256

Find the perimeter of a triangle whose sides are 8n + 5m, - 3n - 4m and 4n + 4m.

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