# One of the legs of a right-angled triangle is 6. the other boat is 8. Find the length of the median drawn to the hypotenuse.

January 14, 2021 | education

| To solve the problem, we use the picture.

Let a right-angled triangle with legs AB = 6 cm and BC = 8 cm be given.

ВO is the median drawn to the hypotenuse.

Find the length of the hypotenuse using the Pythagorean theorem.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 6 ^ 2 + 8 ^ 2 = 36 + 64 = 100.

AC = 10 cm.

Let us complete from triangle ABC a rectangle AВСD, in which ВD and AC are the diagonals of the rectangle, which at the point of their intersection are halved and equal to each other. Then

AC = ВD.

ВO = DO = AO = CO = (1/2) x AC = 10/2 = 5 cm.

Answer: The length of the median ВO = 5 cm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.