Question

Solve the following problems:

The perimeter of an isosceles triangle is $48\mathrm{cm}$. If the length of the unequal side is $17\mathrm{cm}$, find the length of other two equal sides.

Answer 1

Given, The perimeter of an isosceles triangle is $48\mathrm{cm}$ and the length of the unequal side is $17\mathrm{cm}$

Let the length of each equal side of the given isosceles triangle be $\mathrm{x}\mathrm{cm}$

According to the given condition,

The perimeter of the Isosceles triangle $=2\times \mathrm{lenght}\mathrm{of}\mathrm{equal}\mathrm{side}+\mathrm{lenght}\mathrm{of}\mathrm{unequal}\mathrm{side}$

$$\begin{gathered} \Rightarrow 48=2\mathrm{x}+17 \\ \Rightarrow 2\mathrm{x}+17-17=48-17[\mathrm{Subtracting}17\mathrm{from}\mathrm{both}\mathrm{sides}] \\ \Rightarrow 2\mathrm{x}=31 \\ \Rightarrow \frac{2\mathrm{x}}{2}=\frac{31}{2} \\ \therefore \mathrm{x}=15\frac{1}{2}\mathrm{cm} \end{gathered}$$

Hence, the length of the other two equal sides of a given isosceles triangle is $15\frac{1}{2}\mathrm{cm}$.