Question

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

• A. $8p^2+11p-7$
• B. $2p^2+3p+5$
• C. $3p^2+5p-4$
• D. $5p^2-5p+9$

Answer 1

The correct option is B $2p^2+3p+5$

Given perimeter of triangle is $6p^2-4p+9$ and two of its sides are $p^2-2p+1$ and $3p^2-5p+3$.

Let thee third side be $c$.

we k.n.t perimeter of a triangle $p$ with sides $a,b,c$ is $p=a+b+c$.

$p=$$6p^2-4p+9$

$a=$ $p^2-2p+1$

$b=$$3p^2-5p+3$.

$p=a+b+c$

$c=p-a-b$

$c=$($6p^2-4p+9$)-($p^2-2p+1$)-($3p^2-5p+3$)

$c=(6-1-3)p^2+(-4+2+5)p+(9-1-3)$

$\therefore c=2p^2+3p+5$

1. 
   

$\therefore$ third side of given triangle is $2p^2+3p+5$.