Explanation:
Given that,
The area of an isosceles triangle, A = 192 cm²
The ratio of base and height is 3:2.
The area of a triangle is given by :
![A=(1)/(2)* b* h](https://img.qammunity.org/2022/formulas/mathematics/high-school/yhj1jx0u8lezcar5czadn7smtdv43mwuza.png)
Let base = 3x and height = 2x
So,
![192=(1)/(2)* 3x* 2x\\\\3x^2=192\\\\x^2=64\\\\x=8](https://img.qammunity.org/2022/formulas/mathematics/high-school/829f3anyaje5yfpxbqkoo89ujtfh9e9jcs.png)
Base = 3x = 3(8) = 24 cm
Height = 2x = 2(8) = 16 cm
Let equal sides be 16 cm and base be 24
So,
Perimeter = sum of all sides
= 16+16+24
= 56 cm
Hence, this is the required solution.