The perimeter of an isosceles triangle is 16 cm, and its base is 6 cm. Find the bisector of the triangle drawn to the base.

∆АВС – isosceles.

It is known that the perimeter P = AB + BC + AC = 16 cm. AB + BC = 16 – 6 = 10 cm.

Let AB = BC = x. We get x + x = 10 or x = 5cm. So AB = BC = 5 cm.

The bisector in an isosceles triangle is the median and bisects the opposite side. So AH = CH = 3 cm.

The bisector in an isosceles triangle is the height. Hence it follows that ∆АВН is rectangular.

By the Pythagorean theorem, we have AB ^ 2 = AH ^ 2 + BH ^ 2 or BH = √ (AB ^ 2 – AH ^ 2) = √ (5 ^ 2 – 3 ^ 2) = √16 = 4 cm.

Answer: AH = 4 cm.