The diagonal of the slave trapezoid with a base of 8 cm and 5 cm is the bisector of the

The diagonal of the slave trapezoid with a base of 8 cm and 5 cm is the bisector of the acute angle of the trapezoid. Find the perimeter of the trapezoid

Let in an isosceles trapezoid ABCD the sides BC = 5 cm, AD = 8 cm, <BAC = <CAD by condition. From this it follows that the triangle ABC is isosceles, so the angles at the base of the AC are equal. Hence the sides are equal: AB = BC = 5 = CD.
Now we find the perimeter of the trapezoid: perimeter = AB + BC + CD + AD = 5 + 5 + 5 + 8 = 23 (cm), since all calculations are given in centimeters.