In a triangle, length of all the three medians are 9 cm, 12 cm and 15 cm respectively. Then what will be the area of the triangle ? एक त्रिभुज में सभी तीनों माध्यिकाओं क्रमशः 9 सेमी., 12 सेमी. और 15 सेमी. हैं तो त्रिभुज का क्षेत्रफल क्या होगा ?

For a triangle with medians of lengths 9 cm, 12 cm, and 15 cm, these form a right triangle (9² + 12² = 81 + 144 = 225 = 15²). The area of a triangle with medians ma, mb, mc is (4/3) times the area of the triangle formed by the medians. Area of triangle with sides 9, 12, 15 = (1/2) * 9 * 12 = 54 cm². Therefore, area of original triangle = (4/3) * 54 = 72 cm². Option A (36 cm²) is incorrectly calculated without the 4/3 factor. Option C (54 cm²) is the area of the median triangle, not the original triangle. Option D (64 cm²) has no mathematical basis in this problem.