Question

Периметр рівнобедреного трикутника дорівнює 22 см. Основа трикутника на 6 см довша за бічну сторону. Знайдіть сторони трикутника. У трикутника АВС вписано коло яке дотикається до його сторін АВ, АС, ВС відповідно в точках М, N, L. Відрізки АМ, BL, CN відноситься як 2:4:5. Знайдіть периметр трикутника А, В, С, якщо ВС=27 см Скажіть будьласка даю 20 балів срочно!!!!!!!!!!!!!!

Answer 1

Ответ:

Объяснение:

1)

Р=22см

Нехай бічна сторона = х см, тоді основа = (х+8) см.

Складемо і розв'яжемо таке рівняння:

х+х+8=22

2х=14

х=7

Бічна сторона = 7 см,

Основа = 7+8=15 см

2)

Нехай х - коефіцієнт пропорційності

Тоді АМ=2х см, ВL=4x cм, CN=5х см

ВС = 27 см

???

Answer 2

Perimeter of an Isosceles Triangle

To find the sides of an isosceles triangle, we need to use the given information about the perimeter and the relationship between the base and the side.

Let's denote the base of the triangle as b and the length of each side as s.

Given: - Perimeter of the triangle = 22 cm - The base of the triangle is 6 cm longer than the side

To find the sides of the triangle, we can set up an equation using the perimeter:

Perimeter = 2s + b

Substituting the given values: 22 = 2s + (s + 6)

Simplifying the equation: 22 = 3s + 6

Rearranging the equation: 3s = 22 - 6 3s = 16

Dividing both sides by 3: s = 16 / 3

Therefore, the length of each side of the triangle is 16/3 cm.

To find the base of the triangle, we can substitute the value of s into the equation:

b = s + 6 b = (16/3) + 6

Simplifying the equation: b = 16/3 + 18/3 b = 34/3

Therefore, the base of the triangle is 34/3 cm.

Perimeter of Triangle ABC

To find the perimeter of triangle ABC, we need to use the given information about the lengths of the sides and the relationship between the segments AM, BL, and CN.

Given: - Length of segment AM : Length of segment BL : Length of segment CN = 2 : 4 : 5 - Length of segment BC (or VS) = 27 cm

Let's denote the lengths of the segments AM, BL, and CN as a, b, and c respectively.

Using the given ratio, we can express the lengths of the segments as: AM = 2x BL = 4x CN = 5x

We know that the sum of the lengths of the segments AM, BL, and CN is equal to the length of the side BC (or VS): AM + BL + CN = BC

Substituting the values: 2x + 4x + 5x = 27

Simplifying the equation: 11x = 27

Dividing both sides by 11: x = 27 / 11

Therefore, the value of x is 27/11.

To find the lengths of the segments AM, BL, and CN, we can substitute the value of x into the expressions:

AM = 2x = 2 * (27/11) = 54/11 BL = 4x = 4 * (27/11) = 108/11 CN = 5x = 5 * (27/11) = 135/11

Now, we can find the perimeter of triangle ABC by adding the lengths of the sides AB, BC, and AC: Perimeter = AB + BC + AC

Given that BC (or VS) = 27 cm, we need to find the lengths of AB and AC.

Since triangle ABC is an isosceles triangle with sides AB and AC being equal, we can calculate the lengths of AB and AC by adding the lengths of the segments AM, BL, and CN to the length of BC (or VS):

AB = BC + AM = 27 + 54/11 = (297 + 54)/11 = 351/11 AC = BC + CN = 27 + 135/11 = (297 + 135)/11 = 432/11

Now, we can calculate the perimeter of triangle ABC: Perimeter = AB + BC + AC = (351/11) + 27 + (432/11) = (351 + 297 + 432)/11 = 1080/11

Therefore, the perimeter of triangle ABC is 1080/11 cm.

I hope this helps! Let me know if you have any further questions.