In a right-angled triangle ABC, angle C = 90 degrees, angle A = 45 degrees, median

In a right-angled triangle ABC, angle C = 90 degrees, angle A = 45 degrees, median length CM = 6. Find the length BC and the area of the triangle ABC.

The ACM triangle is rectangular and isosceles, since the angle is M = 90, the angle is A = 45.

Then AM = CM = 6 cm, and AC ^ 2 = CM ^ 2 + AM ^ 2 = 36 + 36 = 72.

AC = 6 * √2 cm.

Triangle ABC is also equilateral and rectangular, since angle C = 90, angle A = 45, BC = AC = 6 * √2 cm.

Determine the area of the triangle ABC.

Savs = AC * BC / 2 = 6 * √2 * 6 * √2 / 2 = 36 cm2.

Answer: The length of the BC is 6 * √2 cm, the area of the ABC is 36 cm2.