Given an isosceles trapezoid ABCD, find the middle line of the trapezoid if its perimeter

Given an isosceles trapezoid ABCD, find the middle line of the trapezoid if its perimeter is 34 and the lateral side is 5.

Given:
ABCD – isosceles trapezoid,
P abcd = 34,
AB and CD lateral sides,
AB = CD = 5,
KM is the middle line of this trapezoid.
Find the length of the midline of the KM trapezoid ABCD -?
Decision:
1) Consider an isosceles trapezoid ABCD.
P abcd = AB + BC + CD + AD.
Since AB = CD = 5 and P abcd = 34, then 34 = 5 + BC + 5 + AD, then
AD + BC = 34 – 5 – 5;
AD + BC = 34 – 10;
AD + BC = 24;
2) The middle line of the trapezoid is equal to the half-sum of its bases. Hence
KM = (BC + AD): 2.
Since AD + BC = 24, then KM = (BC + AD): 2 = 24: 2 = 12.
Answer: 12.