Question

Средняя линия трапеции 19см одно и3 основай на 6см меньше другого.Найти основание трапеции.Прошу помогите с решением

Answer 1

Calculation of the Trapezoid's Base

To find the base of a trapezoid, we need to use the given information that the average length of the trapezoid is 19 cm and one base is 6 cm shorter than the other base.

Let's assume the longer base of the trapezoid is represented by x cm. According to the given information, the shorter base will be x - 6 cm.

The formula to calculate the average length of a trapezoid is:

Average Length = (Longer Base + Shorter Base) / 2

Substituting the given values into the formula, we have:

19 = (x + (x - 6)) / 2

To solve for x, we can multiply both sides of the equation by 2:

38 = x + (x - 6)

Simplifying the equation:

38 = 2x - 6

Adding 6 to both sides:

44 = 2x

Dividing both sides by 2:

x = 22

Therefore, the longer base of the trapezoid is 22 cm, and the shorter base is 16 cm (22 - 6).