# In an isosceles triangle ABC with base AC, height BE = 5cm and perimeter = 18cm. What is the perimeter of ABE?

1. In the geometrical figure given according to the condition of the problem, the height performs the functions of the median, that is, it divides the base of the AC into equal segments AE and CE. AC = 2AE.

2. The perimeter of the triangle ABE = AB + BE + AE = AB + AE + 5 cm.

3. The perimeter of the triangle ABC = BC + AC + AB = 18 cm. BC = AB, since the triangle is isosceles. We replace in this expression BC with AB, AC with 2AE:

2AB + 2AE = 18 cm.

AB + AE = 9 cm.

4. Substitute AB + AE = 9 in the first expression: the perimeter of the triangle ABE = 9 + 5 = 14 cm.

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