Semi perimeter of a triangle of sides $2a,\text{ 3}a\text{ and 5}a$ is

Concept: If a triangle has three sides $\mathrm{a}, \mathrm{b},$ and $\mathrm{c}$, semi-perimeter, $\mathrm{s}$, and area of triangle $\mathrm{A}$, then the semi-perimeter and area of the triangle are given as:

$\text{s}=\frac{\text{a}+\text{b}+\text{c}}{2}$

Area of triangle $=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$

Here, sides are $2a,\text{ 3}a\text{ and 5}a$.

Now, $\text{s}=\frac{2a+3a+5a}{2}=5a$

Hence, the semi perimeter of triangle of given sides is  $5a$.