The perimeter of the isosceles triangle ABC with the base BC is 40cm, and the perimeter

The perimeter of the isosceles triangle ABC with the base BC is 40cm, and the perimeter of the equilateral triangle BCD is 45cm. Find sides AB and BC.

According to the condition of the problem, an isosceles triangle ABC with a base BC has a perimeter P = 40 cm.

Consequently,

P = BC + AB + AC = BC + 2 * AB = 40.

It is also known that the perimeter P1 of an equilateral triangle BCD is 45cm.

Consequently,

P1 = BC + CD + BD = 3 * BC = 45. Hence we get: BC = 15.

Then we have:

BC + 2 * AB = 40,

15 + 2 * AB = 40,

2 * AB = 25,

AB = 25/2 = 12.5.

Answer: AB = 12.5 and BC = 15.