Find the length of the lateral side of an isosceles trapezoid if it is equal to its midline

Find the length of the lateral side of an isosceles trapezoid if it is equal to its midline and the perimeter of the trapezoid is 24cm.

Let us denote the lengths of the bases of this isosceles trapezoid by a and b, and the length of the lateral side by x.

According to the condition of the problem, the perimeter of this trapezoid is 24 cm.

Since this trapezoid is isosceles, the lengths of its lateral sides are equal.

Therefore, we can write the following relationship:

a + b + 2x = 24.

Dividing both sides of this ratio by 2, we get:

(a + b + 2x) / 2 = 24/2;

(a + b) / 2 + x = 12.

According to the condition of the problem, the length of the lateral side of this isosceles trapezoid is equal to its midline.

Since the middle line of any trapezoid is equal to the half-sum of its bases, then in this trapezoid (a + b) / 2 = x.

Substituting the found value (a + b) / 2 into the equation (a + b) / 2 + x = 12, we get:

x + x = 12;

2x = 12;

x = 12/2;

x = 6.

Answer: the length of the lateral side of this isosceles trapezoid is 6.