Step-by-step 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 :
[tex]A=\dfrac{1}{2}\times b\times h[/tex]
Let base = 3x and height = 2x
So,
[tex]192=\dfrac{1}{2}\times 3x\times 2x\\\\3x^2=192\\\\x^2=64\\\\x=8[/tex]
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.
