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

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Solution

Perimeter of a triangle = $6 p^{2} - 4 p + 9$
sum of two sides of it = $3 p^{2} - 5 p + 3 + p^{2} - 2 p + 1 = 4 p^{2} - 7 p + 4$
$∴$ Third side $= (6 p^{2} - 4 p + 9 - (4 p^{2} - 7 p + 4)$
$= 6 p^{2} - 4 p + 9 - 4 p^{2} + 7 p - 4 = 2 p^{2} + 3 p + 5$

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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.

Perimeter of a triangle =6p2−4p+9 sum of two sides of it =3p2−5p+3+p2−2p+1=4p2−7p+4 ∴ Third side =(6p2−4p+9−(4p2−7p+4) =6p2−4p+9−4p2+7p−4=2p2+3p+5

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

Perimeter of a triangle = $6 p^{2} - 4 p + 9$
sum of two sides of it = $3 p^{2} - 5 p + 3 + p^{2} - 2 p + 1 = 4 p^{2} - 7 p + 4$
$∴$ Third side $= (6 p^{2} - 4 p + 9 - (4 p^{2} - 7 p + 4)$
$= 6 p^{2} - 4 p + 9 - 4 p^{2} + 7 p - 4 = 2 p^{2} + 3 p + 5$