Question

В равнобокой трапеции основания равны 10см и 24см , боковая сторона 25см. Вычислите высоту трапеции, среднюю линию трапеции. с условиями умоляю если без условий лучше не пишите. Спасибо

Answer 1

Дано: АВСД- трапеция. АВ=СД=25 см, ВС=10 см, АД=24 см
BK_|_АД, РМ - средняя линия
найти: РМ, ВК
решение.
дополнительное построение: CX_|_АД
КХ=7 см, АК=ХД=(24-10):2=7 (см)
рассмотрим ΔАВК: АВ=25 см, АК=7 см, <AKB=90°
по теореме Пифагора:
AB²=AK²+BK²
25²=7²+BK², BK=24 cм
РМ=(АД+ВС)/2,  РМ=(24+10)/2, РМ=17 см
ответ: высота трапеции  =24 см
средняя линия =17 см

Answer 2

Calculation of the Height and Midline of a Trapezoid

To calculate the height and midline of a trapezoid, we need to know the lengths of the bases and one of the lateral sides. In this case, the lengths of the bases are given as 10 cm and 24 cm, and the length of the lateral side is given as 25 cm.

To find the height of the trapezoid, we can use the Pythagorean theorem. The height is the perpendicular distance between the bases of the trapezoid. Let's denote the height as h.

Using the Pythagorean theorem, we can write:

h^2 = (25^2) - ((24 - 10)^2)

Simplifying the equation:

h^2 = 625 - 14^2

h^2 = 625 - 196

h^2 = 429

Taking the square root of both sides:

h ≈ √429

Using a calculator, we find that h ≈ 20.71 cm.

Now, let's calculate the midline of the trapezoid. The midline is the average of the lengths of the bases. Let's denote the midline as m.

m = (10 + 24) / 2

m = 34 / 2

m = 17 cm

Therefore, the height of the trapezoid is approximately 20.71 cm and the midline is 17 cm.

Please note that the sources provided do not contain relevant information for this specific calculation.