Point M is the middle of the AC side of the ABC triangle, in which AB = 6 cm.

Point M is the middle of the AC side of the ABC triangle, in which AB = 6 cm. The perimeter of the triangle ABM and BCM differs by 10 cm. find the side of the sun.

Given:
triangle ABC,
point M – the middle of the AC side,
AB = 6 centimeters,
P ABM – P BCM = 10 centimeters.
Find the length of the BC side -?
Decision:
1) Consider the triangle ABC. Since point M is the middle of the AC side, AM = MC.
2) Consider the triangle ABM. Its perimeter is:
R ABM = AB + BM + AM,
P ABM = 6 + BM + AM.
3) Consider the BCM triangle. Its perimeter is:
P BCM = BC + MC + BM;
R BCM = BC + AM + BM.
4) P ABM – P BCM = 6 + BM + AM – (BC + AC + BM) = 6 + BM + AM – BC – AM – BM = 6 – BC;
10 = 6 – BC;
BC = 10 + 6;
BC = 16 centimeters.
Answer: 16 centimeters.