Question

In $△$PQR, PQ = 4 cm and QR = 6 cm. What can be the length of the third side PR. Find the minimum and maximum possible lengths of side PR.

Answer 1

$$\begin{gathered} \mathrm{In}△\mathrm{PQR},\mathrm{PQ}=4\mathrm{cm},\mathrm{QR}=6\mathrm{cm} \\ \mathrm{We}\mathrm{know}\mathrm{that}\text{the}\mathrm{sum}\mathrm{of}\mathrm{any}\mathrm{two}\mathrm{sides}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{is}\mathrm{greater}\mathrm{than}\mathrm{the}\mathrm{third}\mathrm{side}\mathrm{and} \\ \mathrm{difference}\mathrm{of}\mathrm{any}\mathrm{two}\mathrm{sides}\mathrm{of}\mathrm{a}\mathrm{triangle}\mathrm{is}\mathrm{less}\mathrm{than}\mathrm{the}\mathrm{third}\mathrm{side}. \\ \mathrm{Thus}, \\ \mathrm{PR}<\mathrm{PQ}+\mathrm{QR}=10 \\ \mathrm{and}\mathrm{PR}>\mathrm{QR}-\mathrm{PQ}=2 \\ \text{T}\mathrm{herefore},2<\mathrm{PR}<10. \end{gathered}$$