Question

медиана треугольника с биссектрисой пересекаются под углом 90 градусов сторона к которой провели медиану равна 6 Найди остальные стороны треугольника если известно что сторона к которой провели биссектрису на 3 см больше третьей стороны В ответе запиши значения в порядке возрастания через точку с запятой Пожалуйста помогите это очень срочно!

Answer 1

Ответ:

3 см, 6см

Объяснение:

Рассмотрим треугольник ABM. Биссектриса АО является также высотой (медиана треугольника с биссектрисой пересекаются под углом 90 градусов).

• Если высота треугольника совпадает с его биссектрисой, то такой треугольник — равнобедренный.

=>АВ=АМ=АС/2=6/2=3 см

Так как сторона ВС, к которой провели биссектрису на 3 см больше АВ, то ВС=3×3=6см

Answer 2

Median Triangle with an Intersecting Bisector

To find the lengths of the sides of a triangle with a median and a bisector intersecting at a right angle, we are given the following information:

- One side of the triangle, to which the median is drawn, has a length of 6. - The side to which the bisector is drawn is 3 cm longer than the third side.

Let's denote the sides of the triangle as follows: - The side to which the median is drawn: a (length = 6) - The side to which the bisector is drawn: b (length = a + 3) - The third side: c

To find the lengths of the sides, we can use the properties of a median and a bisector in a triangle.

Properties of a Median in a Triangle

- A median divides the opposite side into two equal segments. - The length of a median is equal to half the length of the opposite side.

Using these properties, we can determine the length of the third side (c) in terms of a:

- The length of the third side (c) is equal to twice the length of the median (a): c = 2a.

Properties of a Bisector in a Triangle

- A bisector divides the opposite side into two segments proportional to the adjacent sides. - The length of the segment of the opposite side adjacent to the bisector is equal to the product of the lengths of the adjacent sides, divided by the sum of the lengths of the adjacent sides.

Using these properties, we can determine the length of the side to which the bisector is drawn (b) in terms of a:

- The length of the side to which the bisector is drawn (b) is equal to the product of the lengths of the adjacent sides (a and c), divided by the sum of the lengths of the adjacent sides (a + c): b = (a * c) / (a + c).

Substituting the value of c from the first equation into the second equation, we can express b in terms of a:

- b = (a * 2a) / (a + 2a) = 2a^2 / 3a = 2a / 3.

Now, we can solve for a by equating the expression for b to the given value of 6:

- 2a / 3 = 6. - Multiplying both sides by 3: 2a = 18. - Dividing both sides by 2: a = 9.

Therefore, the length of the side to which the median is drawn (a) is 9 cm.

Using this value, we can find the length of the side to which the bisector is drawn (b):

- b = 2a / 3 = 2 * 9 / 3 = 6.

Therefore, the length of the side to which the bisector is drawn (b) is 6 cm.

Finally, we can find the length of the third side (c) using the equation c = 2a:

- c = 2 * 9 = 18.

Therefore, the length of the third side (c) is 18 cm.

In summary, the lengths of the sides of the triangle are as follows: - Side to which the median is drawn (a): 9 cm - Side to which the bisector is drawn (b): 6 cm - Third side (c): 18 cm

Please let me know if you need any further assistance!