Find the midline of an isosceles trapezoid whose perimeter is 24 if the side is 5.

1. In an isosceles trapezoid ABCD, the sides are equal:

AB = CD = 5.

2. The perimeter of the trapezoid is equal to the sum of all sides:

P = AB + BC + CD + DA = 24, hence

BC + DA = 24 – (AB + CD);

BC + DA = 24 – (5 + 5);

BC + DA = 24 – 10;

BC + DA = 14.

3. The middle line of the trapezoid is equal to the half-sum of the bases:

PQ = 1/2 * (BC + DA) = 1/2 * 14 = 7.

Answer: 7.