If the given figure, in a right angle triangle ABC, AB = 12 cm and AC = 15 cm. A square is inscribed in the triangle. One of the vertices of square coincides with the vertex of triangle. What is the maximum possible area (in cm²) of the square?

A. $$\frac{{1296}}{{49}}$$

B. $$25$$

C. $$\frac{{1225}}{{36}}$$

D. $$\frac{{1225}}{{64}}$$

Answer: Option A

Solution (By Examveda Team)

Then BC = 9 cm
Side (a) square $$ = \frac{{12 \times 9}}{{21}} = \frac{{36}}{7}$$
Area of largest square that can be formed inside the circle $$ = {\left( {\frac{{36}}{7}} \right)^2} = \frac{{1296}}{{49}}$$