The perimeter of a triangle is $9 m^{2} - 2 n + 8$ and its two sides are $4 m^{2} + 3 n$ and $7 m^{2} + 5 n - 12$ . Find the third side of the triangle.

m^{2} - 10 n - 10

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- 2 m^{2} - 10 n + 20

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- 2 m^{2} - 14 n + 20

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m^{2} - 10 n + 10

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Solution

The correct option is B $- 2 m^{2} - 10 n + 20$
Perimeter of a triangle is $a + b + c$ (side+base+side)
Here, Perimeter is $9 m^{2} - 2 n + 8$
and two sides are $4 m^{2} + 3 n$ , $7 m^{2} + 5 n - 12$
Let other side be $x$
Therefore,
$p e r i m e t e r = a + b + c$
$=> 9 m^{2} - 2 n + 8 = 4 m^{2} + 3 n + 7 m^{2} + 5 n - 12 + x$
$= 9 m^{2} - 2 n + 8 - 4 m^{2} - 3 n - 7 m^{2} - 5 n + 12 = x$
$= - 2 m^{2} - 10 n + 20 = x$
Therefore,
the other side is $- 2 m^{2} - 10 n + 20$

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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 $4 m^{2} + 12$ .

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

2 m^{2} - 10 m n - 2 m + 10 n

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