The perimeter of an isosceles trapezoid is 27. Find the length of its midline if the side length is 7.

Isosceles is a trapezoid in which the sides are equal:

AB = CD.

The midline of a trapezoid is a line segment connecting the midpoints of the sides of the trapezoid. The middle line of the trapezoid is parallel to the bases, and its length is equal to the half-sum of the bases:

m = 1/2 (a + b), where:

m is the middle line of the trapezoid;

a – smaller base of the BC;

b – larger AD base.

In order to find the length of the midline of a trapezoid, you need to calculate the sum of its bases (BC + AD).

Since the trapezoid is isosceles, then:

AB = CD = 7 cm.

The perimeter of a trapezoid is the sum of all its sides:

P = AB + BC + CD + AD;

(BC + AD) = P – (AB + CD);

(ВС + АD) = 27 – (7 + 7) = 27 – 14 = 13 cm.

m = (BC + AD) / 2;

m = 13/2 = 6.5 cm.

Answer: The length of the middle line of the trapezoid is 6.5 cm.