In the triangle ABC, BN, CK are the medians, E is the point of their intersection. BN = 12 cm, CK = 18 cm.

| August 1, 2021 | education

In the triangle ABC, BN, CK are the medians, E is the point of their intersection. BN = 12 cm, CK = 18 cm. The perimeter of the triangle BЕК is 21 cm. Find the length of the side AB.

This problem is on the property of the median in a triangle: the point of intersection of the medians of a triangle divides them into parts. In a ratio of 2 to 1 counting from the vertex.
And the side AB itself is divided by the median CK into two equal parts AK = BK.
Hence, considering the triangle BЕК, we see that all of its sides can be determined.
EK = 1/3 (CK) = 1/3 * 18 = 6 (cm),
BE = BН * (2/3) = 12 * (2/3) = 8 (cm).

The perimeter of the triangle BEC = BE + EK + BK = 21. From here we find half of AB: BK = 1/2 * AB = 21 – 8 – 6 = 7 (cm).
AB = 2 * BK = 2 * 7 = 14 (cm).



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