In triangle ABC, medians AM, BN and CK are drawn. AK = 2, BM = 3, CN = 4 find the perimeter of the triangle.

Given:

triangle ABC,

medians AM, BN and CK,

AK = 2,

BM = 3,

CN = 4.

Find the perimeter of triangle ABC -?

Solution:

Consider a triangle ABC. Since AM is the median, then BM = MC = 3 and BC = 2 * 3 = 6.

Since SC is the median, then AK = KB = 2 and AB = 2 * 2 = 4.

Since BN is the median, then AN = NC = 4 and AC = 4 * 2 = 8.

The perimeter of a triangle is the sum of the lengths of all sides of the triangle. Then P ABC = AB + BC + AC.

P ABC = 4 + 6 + 8;

P ABC = 18.

Answer: The perimeter of triangle ABC is 18.