Given an isosceles triangle to the base of 12cm and the lateral side of 18cm. the segments of what length should

Given an isosceles triangle to the base of 12cm and the lateral side of 18cm. the segments of what length should be set aside from the apex of the triangle on its lateral sides in order to connect their ends to obtain trepez with a perimeter equal to 40 cm.

The segments laid down on the sides and the smaller base of the trapezoid form an isosceles triangle similar to the given one. We take the length of the segments as x, then the smaller base is:

12 * x / 18.

Since the perimeter is equal to the sum of the sides, we get the equation:

2 * (18 – x) + 12 * x / 18 + 12 = 40;

36 – 2x + 3 / 4x + 12 = 40;

4 / 3x = 8;

x = 3 * 8/4 = 6 cm.

Answer: the desired length of the segments is 6 cm.