The bisector of a triangle divides its sides into segments 5 cm and 6 cm long.

The bisector of a triangle divides its sides into segments 5 cm and 6 cm long. Find the area of the triangle if the smaller of the other two sides is 15 cm.

One of the properties of the bisector is the following: “the bisector divides the opposite side into parts proportional to the adjacent sides.”

By this property: ВL / AB = LC / AC = 5/15 = 1/3.

Hence, LC / AC = 1/3 => 6 / AC = 1/3

According to the rule of proportion AC = (3 * 6) / 1 = 18 cm.

Answer: 18 cm.




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