Question

Perimeter of an isosceles triangle is 50cm. if one of the two equal sides is 18cm, find the third.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{ABC}\mathrm{be}\mathrm{the}\mathrm{isosceles}∆\mathrm{in}\mathrm{which}\mathrm{AB}=\mathrm{AC}. \\ \mathrm{Let}\mathrm{AB}=\mathrm{AC}=18\mathrm{cm} \\ \mathrm{Perimeter}\mathrm{of}∆\mathrm{ABC}=50\mathrm{cm} \\ \Rightarrow \mathrm{AB}+\mathrm{BC}+\mathrm{AC}=50 \\ \Rightarrow 18+\mathrm{BC}+18=50 \\ \Rightarrow 36+\mathrm{BC}=50 \\ \Rightarrow \mathrm{BC}=50-36 \\ \Rightarrow \mathrm{BC}=14\mathrm{cm} \\ \mathrm{So},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{third}\mathrm{side}=14\mathrm{cm} \end{gathered}$$