In an isosceles triangle ABC (AB = BC), [CD] is the height. Point D divides the side [AB] into segments AD

In an isosceles triangle ABC (AB = BC), [CD] is the height. Point D divides the side [AB] into segments AD = 2cm and BD = 8cm. Find the perimeter of triangle ABC.

To begin with, we find the side AB: AB = AD + DB = 2 + 8 = 10. Under the condition of the problem AB = BC.

Consider the triangle ВDC and by the Pythagorean theorem we find DC: DC = √ (ВС ^ 2 – DB ^ 2) = √ (100 – 64) = 6.

Similarly, we find AC: AC = √ (DC ^ 2 + AD ^ 2) = √ (36 + 4) = 2√10.

P = 2√10 + 10 + 10 = 20 + 2√10.

Answer: P = 20 + 2√10.