Since CM is the bisector of an angle, then by the property of the bisector of a triangle: AC / AM = BC / BM.
AC / 15 = BC / 20.
AC / 3 = BC / 4.
AC / BC = 3/4.
Let the length of the AC segment be 3 * X cm, then the length of the BC segment = 4 * X cm.
The length of the hypotenuse AB = AM + BM = 15 + 20 = 35 cm.
In a right-angled triangle ABC, according to the Pythagorean theorem:
AB ^ 2 = AC ^ 2 + BC ^ 2.
1225 = 9 * X ^ 2 + 16 * X ^ 2.
25 * X ^ 2 = 1225.
X ^ 2 = 1225/25 = 49.
X = 7 cm.
AC = 3 * 7 = 21 cm.
BC = 4 * 7 = 28 cm.
Then the area of the triangle is equal to: Sавс = АС * ВС / 2 = 21 * 28/2 = 294 cm2.
Answer: The area of triangle ABC is 294 cm2.
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