The corresponding sides of two similar triangles are 2 cm and 4 cm respectively. If the area of first triangle is 36 sq.cm, then the area of second triangle is:

Let A and B are areas of the first and second triangle respectively.

From the question, we have 
Area of first triangle (A) = 36 sq.cm

As we know that,

The ratio of the areas of two similar triangles is equal to the square of the ratio of their
corresponding sides.

Then,

$\frac{B}{A} = {\left(\frac{side of second triangle}{side of first triangle}\right)}^2$

$\frac{B}{36} = {\left(\frac{4}{2}\right)}^2$

$\frac{B}{36} = \frac{16}{4}$

$B= \frac{36\times 16}{4}= 144 sq.cm$

Hence the area of second triangle is 144 sq.cm.