Question

The perimeter of a tringle 6p² -4p² +9 and its two sides are p²- 2p+1 amd 3p²-5p+3. Find third side of tringle.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{a}={\mathrm{p}}^2-2\mathrm{p}+1 \\ \mathrm{b}=3{\mathrm{p}}^2-5\mathrm{p}+3 \\ \mathrm{c}=? \\ \mathrm{Now},\mathrm{perimeter}\mathrm{of}∆=6{\mathrm{p}}^2-4\mathrm{p}+9 \\ \Rightarrow \mathrm{a}+\mathrm{b}+\mathrm{c}=6{\mathrm{p}}^2-4\mathrm{p}+9 \\ \Rightarrow \left({\mathrm{p}}^2-2\mathrm{p}+1\right)+\left(3{\mathrm{p}}^2-5\mathrm{p}+3\right)+\mathrm{c}=6{\mathrm{p}}^2-4\mathrm{p}+9 \\ \Rightarrow \left(4{\mathrm{p}}^2-7\mathrm{p}+4\right)+\mathrm{c}=6{\mathrm{p}}^2-4\mathrm{p}+9 \\ \Rightarrow \mathrm{c}=\left(6{\mathrm{p}}^2-4\mathrm{p}+9\right)-\left(4{\mathrm{p}}^2-7\mathrm{p}+4\right)=2{\mathrm{p}}^2+3\mathrm{p}+5 \end{gathered}$$