Question

Основание пирамиды- треугольник с катетами 6 и 8 см. Высота пиромиды проходит через середину гипотенузы и равна гипотенузе. Найти боковые ребра пиромиды

Answer 1

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Треугольник  с  катетами  6  и  8  см-- египетский,   значит   гипотенуза   равна  10  см. 

 

Боковые  ребра  с  вершинами   на  гипотенузе  будут  равны

 

V100  -  25  =  V75  =  5V3(см)

 

 

S треуг  =  1/2 *6*8  =  1/2 *10*х,  где  х -  перпендикуляр,   опущенный  из 

 

вершины  прямого  угла  на  гипотенузу

 

Получим    х  =  4,8 см

 

Боковое  ребро  выходящее  из  вершины   прямого  угла  будет  равно

 

V100  -  4.8^2  =  V76.96  =  4V4.81(см)

 

Ответ.  5V3см     5V3см   и   4V4,81   cм

Answer 2

Calculation of the Side Lengths of the Pyramid

To find the side lengths of the pyramid, we can use the given information about the base and the height.

The base of the pyramid is a right triangle with legs measuring 6 cm and 8 cm. The height of the pyramid passes through the midpoint of the hypotenuse and is equal to the hypotenuse itself.

Let's denote the side lengths of the pyramid as follows: - The base side lengths: AB = 6 cm and BC = 8 cm. - The height of the pyramid: AH = BH = CH = DH = hypotenuse of the base triangle.

To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse (AH): AH = √(AB^2 + BC^2)

Substituting the given values: AH = √(6^2 + 8^2) AH = √(36 + 64) AH = √100 AH = 10 cm

Since the height of the pyramid is equal to the hypotenuse, the side lengths of the pyramid are as follows: - The base side lengths: AB = 6 cm and BC = 8 cm. - The height and the side lengths of the pyramid: AH = BH = CH = DH = 10 cm.

Therefore, the side lengths of the pyramid are 6 cm, 8 cm, and 10 cm.