$$\triangle$$ABC $$\sim$$ $$\triangle$$NLM and ar($$\triangle$$ABC): ar($$\triangle$$NLM) = 4 : 9. If AB = 6 cm, BC = 8 cm and AC =12 cm, then ML is equal to:

Theorem: If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. This proves that the ratio of areas of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

As $$\triangle$$ABC $$\sim$$ $$\triangle$$NLM

$$\frac{\triangle ABC}{\triangle NLM} = \frac{BC^2}{LM^2} $$

$$\frac{2}{3} = \frac{BC}{LM}$$

$$\frac{2}{3} = \frac{8}{LM}$$

So , LM =12 cm

So , the answer would be option d)12 cm.