Given a triangle with sides 15,15 and 24, find the distances from the intersection of the medians to the sides of the triangle.

univerkov | April 13, 2021 | education

The height of the ВН of an isosceles triangle is also its median, then AH = CH = AC / 2 = 24/2 = 12 cm.

In a right-angled triangle ABН, according to the Pythagorean theorem, BH^2 = AB^2 – AH^2 = 225 – 144 = 81.

BH = 9 cm.

Point O divides the median BH in the ratio of 2/1, then OH = BH * 1/3 = 9/3 = 3 cm.

Savn = AH * ВН / 2 = 12 * 9/2 = 54 cm2.

Saon = AH * OH / 2 = 12 * 3/2 = 18 cm2.

Saov = Saun – Saon = 54 – 18 = 36 cm2.

Also Saov = AB * OM / 2.

OM = 2 * Saos / AB = 2 * 36/15 = 4.8 cm.

ОР = OM = 4.8 cm.

Answer: From point M to the sides of the triangle 3 cm, 4.8 cm, 4.8 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.