Question

В ранобедренной трапеции высота делит болшееоснование на отрезки , равные 5 и 12 см. Найдите среднюю линию трапеции.

Answer 1

Дана равнобедренная трапеция АВСД. Высота ВК делит АД на АК=5см и КД=12см.

Следовательно большее основание =5+12=17см

Если провести вторую высоту СР из вершины С, то получим, что АК=РД=5 см.

КР=ВС=12-5=7см (по сво-вам равнобедренной трапеции)

 

Средняя линия =(7+17):2=12 см

Answer 2

Finding the Midline of a Trapezoid

To find the midline of a trapezoid, we need to know the lengths of the two bases and the height. In this case, we are given that the height divides the larger base into segments of 5 cm and 12 cm.

Let's denote the lengths of the two bases as a and b, and the height as h. We are given that h divides the larger base into segments of 5 cm and 12 cm.

Using this information, we can set up the following equation:

a + b = 5 + 12

Simplifying the equation, we have:

a + b = 17

Since we are looking for the midline, which is the average of the two bases, we can divide the sum of the bases by 2:

midline = (a + b) / 2

Substituting the value of the sum of the bases, we have:

midline = 17 / 2

Simplifying further, we find:

midline = 8.5 cm

Therefore, the midline of the trapezoid is 8.5 cm.