Question

Диагональ трапеции делит среднюю линию на отрезки длины которых равны 6 см и 10 см. вычислите длины оснований трапеции ))) пожалуйста

Answer 1

Отрезки средней линии трапеции являются средними линиями в треугольниках, образованными диагональю. Средняя линия треугольника равна половине основания. Основания в треугольниках являются основаниями трапеции.   1)10х2=20(см)-большее основание.    2) 6х2=12(см)-меньшее основание.

Answer 2

Calculating the Lengths of the Bases of a Trapezoid

To calculate the lengths of the bases of the trapezoid, we can use the properties of a trapezoid and the given information about the diagonals and the segments they divide.

Given: - The diagonal of the trapezoid divides the median into segments of length 6 cm and 10 cm.

Solution:

Let's denote the lengths of the bases of the trapezoid as \( a \) and \( b \), and the length of the median as \( m \).

According to the properties of a trapezoid, the median can be expressed in terms of the lengths of the bases as: \[ m = \frac{a + b}{2} \]

Given that the diagonal divides the median into segments of length 6 cm and 10 cm, we can express the median as the sum of these segments: \[ m = 6 + 10 \] \[ m = 16 \]

Substituting the value of \( m \) into the equation for the median, we get: \[ 16 = \frac{a + b}{2} \]

Solving for \( a + b \), we have: \[ a + b = 32 \]

Since the sum of the lengths of the bases is 32, and the difference between the lengths of the bases is equal to the difference between the segments of the median, we can set up the following system of equations: \[ \begin{cases} a + b = 32 \\ a - b = 4 \end{cases} \]

Solving this system of equations, we find: \[ a = 18 \] \[ b = 14 \]

Answer:

Therefore, the lengths of the bases of the trapezoid are: - \( a = 18 \) cm - \( b = 14 \) cm