In an isosceles triangle ABC with a base AC, the height BE is 5 cm, and the perimeter

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

1. The perimeter of the triangle ABE = AB + AE + BE.

2. The perimeter of the triangle ABC = AB + BC + AC = 18 cm.

3. AB = BC as lateral sides of an isosceles triangle.

4. AE = CE, since the height BE is also the median and divides the AC in half.

5. AE + CE = AC. AC = 2AE.

6. In the second formula, replace BC with AB, AC with 2AE:

2AB + 2AE = 18 cm.Divide this expression by 2:

AB + AE = 9 cm. Substitute in the first formula:

The perimeter of the triangle ABE = 9 + 5 = 14 cm.

Answer: the perimeter of the triangle ABE = 14 cm.