In an isosceles triangle ABC with the base of the AC, the height BD was drawn.

In an isosceles triangle ABC with the base of the AC, the height BD was drawn. Find the perimeter of the triangle ABC if BD = 10 cm and the perimeter of the triangle ABD = 40 cm.

Perimeter of a triangle P = ABD = AB + BD + AD;

the perimeter of the triangle P ‘= BCD = BC + BD + CD;

P = P ‘, since AB = BC, AD = CD;

P + P ‘= AB + BD + AD + BC + BD + CD = AB + BC + (AD + CD) + 2 * BD;

AD + CD = AC; 2 * P = AB + BC + AC + 2 * BD;

The perimeter of the triangle ABC P ” = AB + BC + AC;

P ” = 2 * P – 2 * BD = 2 * 40 – 2 * 10 = 60 (cm).