Since the triangle ABC is rectangular, and the angle ABC = 450, this triangle is isosceles, AC = AB.
Then, by the Pythagorean theorem, AB ^ 2 = AC ^ 2 + BC ^ 2 = 2 * AC ^ 2.
2 * AC ^ 2 = 32.
AC ^ 2 = 32/2 = 16.
AC = BC = 4 cm.
Determine the area of the triangle ABC.
Savs = AC * BC / 2 = 4 * 4/2 = 8 cm2.
Since triangle ABC is isosceles, the median CM is also the height of triangle ABC.
Then Saws = CM * AB / 2.
CM = 2 * Savs / AB = 2 * 8/4 * √2 = 4 / √2 = 2 * √2 cm.
Answer: The area of the triangle is 8 cm2, the length of the median is 2 * √2 cm.
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