Question

The semi-perimeter of an isosceles triangle is 12 cm. The length of its unequal side is 10 cm.

What is the length of each equal side of the triangle?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{equal}\mathrm{sides}\mathrm{of}∆\mathrm{be}x\mathrm{cm}. \\ \mathrm{Now},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{unequal}\mathrm{side}=10\mathrm{cm} \\ \mathrm{Let}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}\mathrm{represent}\mathrm{the}\mathrm{sides}\mathrm{of}∆. \\ \mathrm{Now},a=b=x\mathrm{cm} \\ \mathrm{and}\mathrm{c}=10\mathrm{cm} \\ \mathrm{Now},\mathrm{semi}\mathrm{perimeter}\mathrm{of}∆=12\mathrm{cm} \\ \Rightarrow \frac{a+b+c}{2}=12 \\ \Rightarrow x+x+10=24 \\ \Rightarrow 2x+10=24 \\ \Rightarrow 2x=24-10 \\ \Rightarrow 2x=14 \\ \Rightarrow x=\frac{14}{2} \\ \Rightarrow x=7 \\ \mathrm{Now},\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{equal}\mathrm{sides}\mathrm{of}\mathrm{isosceles}∆\mathrm{is}7\mathrm{cm}. \end{gathered}$$