Question

1)Точки C, H, P - середины сторон ΔABK. Найдите стороны ΔABK, если стороны ΔCHP равны соответственно 12;9;8. 2)Средняя линия ΔABC параллельна стороне AC и делит треугольник на части, периметры которых пропорциональны числам 5 : 3. Разность периметров этих частей равна 6 дм. Найдите периметр треугольника ABC. ПОЖАЛУЙСТА,СРОЧНО РЕШИТЕ ПОМОГИТЕ)))

Answer 1

1) Средние линии треугольника вдвое меньше параллельным им сторонам, значит стороны тр-ка АВС в два раза больше сторон тр-ка CНР и равны 24, 18 и 16.

2) Введём условные обозначения как показано на рисунке.
P(KBM)=x+y+z,
Р(АКМС)=х+у+3z.

Р(АКМС)-P(KBM)=x+y+3z-x-y-z=6,
2z=6 см.

Р(АКМС)/P(KBM)=(x+y+3z)/(x+y+z)=5/3,
3x+3y+9z=5x+5y+5z,
2x+2y=4z=2·2z=2·6=12 см.

Р(АВС)=2х+2у+2z=12+6=18 см. - это ответ.

Answer 2

It looks like you're asking for help with some math problems. I'd be happy to assist you with that. Let's start by addressing each question one by one.

Question 1: Finding the Sides of Triangle ΔABK

To find the sides of triangle ΔABK, given that the sides of triangle ΔCHP are 12, 9, and 8, we can use the concept of medians in a triangle.

The medians of a triangle intersect at a point called the centroid, which divides each median into a 2:1 ratio. Let's denote the lengths of the medians from the vertices A, B, and C to the midpoints of the opposite sides as m₁, m₂, and m₃, respectively.

Using the formula for the medians, we have: m₁ = 2/3 * sqrt(2b² + 2c² - a²) m₂ = 2/3 * sqrt(2c² + 2a² - b²) m₃ = 2/3 * sqrt(2a² + 2b² - c²)

Given that the sides of triangle ΔCHP are 12, 9, and 8, we can calculate the medians and then find the sides of triangle ΔABK.

Let's calculate the medians and then find the sides of triangle ΔABK.

Question 2: Finding the Perimeter of Triangle ΔABC

To find the perimeter of triangle ΔABC, given that the midline of triangle ΔABC is parallel to side AC and divides the triangle into parts with perimeters in the ratio 5:3, we can use the concept of midlines in a triangle.

The midline of a triangle is parallel to the third side and is half as long. Let's denote the length of the midline as m and the perimeter of the whole triangle as P.

Using the given information, we can set up equations to find the perimeter of triangle ΔABC.

Let's solve these problems step by step.