ΔABC ∼ ΔDEF and the perimeters of these triangles are 32 cm and 12 cm respectively. If DE = 6 cm, then what will be the length of AB ?

16 cm

We know that,

The ratio of the sides of a triangle = The ratio of the perimeter of that triangle

So, according to the question,

\(\frac{AB}{DE}\) = \(\frac{32}{12}\)  

\(\frac{AB}{6}\) = \(\frac{32}{12}\) 

AB = 16 cm