Question

Дан прямоугольник АВСД. Биссектриса угла В пересекает сторону АД в точке М так, что АМ : МД = 2 : 3. Найдите стороны прямоугольника, если его периметр равен 56см.​

Answer 1

Ответ:Биссектриса отсекает от прямоугольника равнобедренный треугольник,где

АВ=АМ=2 части

АD=2+3=5 частей

2•2+5•2=14 частей

Одна часть равна

56:14=4 см

АВ=СD=4•2=8 cм

ВС=АD=4•5=20 cм

Проверка

8•2+20•2=16+40=56 см

Можно решить через Х

Одна сторона 2Х

Вторая сторона 5Х

2Х•2+5Х•2=56

14Х=56

Х=56:14

Х=4

Одна сторона 4•2=8 см

Вторая 4•5=20 см

Противоположные стороны прямоугольника равны между собой

Объяснение:

Answer 2

Let's denote the length of side AD as x, and the length of side AB as y.

Since AM:MD = 2:3, we can write the following equation:

AM/MD = 2/3 AM = 2/3 * MD

Since AM + MD = AD, we can substitute the value of AM in terms of MD:

(2/3 * MD) + MD = x 5/3 * MD = x

We also know that the perimeter of the rectangle is equal to 56 cm. So we can write the equation:

2x + 2y = 56

Now we can solve the system of equations formed by the above two equations:

5/3 * MD + MD = x ------(1) 2x + 2y = 56 ------(2)

From equation (1), we can simplify it to:

8/3 * MD = x MD = 3/8 * x

Substituting this value in equation (2) and solving for x:

2(5/3 * MD) + 2y = 56 10/3 * MD + 2y = 56 10/3 * (3/8 * x) + 2y = 56 5/4 * x + 2y = 56

Now, let's simplify this equation further:

5/4 * x + 2y = 56 5x/4 + 2y = 56 5x + 8y = 224

Now we have two equations:

5x + 8y = 224 ------(3) 8x = 3x ---------from x = 8/3 * MD

Simplifying equation (3):

5x + 8y = 224 (40/3 * MD) + 8y = 224 40/3 * MD + 8y = 224 40/3 * MD + 8y = 224 (40/3) * (3/8 * x) + 8y = 224 5x + 8y = 224

Since equation (3) is the same as equation (3), we can conclude that there are infinitely many possible values for x and y that satisfy the given conditions. Therefore, we cannot determine the specific lengths of the sides of the rectangle.