Question

отрезок АВ,точка R поделили пополам.АВ=24 см.Точка М лежит на отрезке AR.Найти: АМ,МR,МВ,если АМ в 3 раза больше отрезка МR

Answer 1

Пусть отрезок AM равен 3x см, где x - длина MR в сантиметрах.

Тогда отрезок MR будет равен x см, и AM будет равен 3x см.

Сумма AM и MR должна равняться длине отрезка AR, который равен половине отрезка AB:

AM + MR = AR = (1/2) * AB

AM + x = (1/2) * 24

AM + x = 12

Теперь у нас есть два уравнения:

AM = 3x
AM + x = 12
Мы можем решить эту систему уравнений:

Из уравнения 2 выразим x:

x = 12 - AM

Подставим это значение в уравнение 1:

AM = 3(12 - AM)

AM = 36 - 3AM

4AM = 36

AM = 9 см

Теперь, когда мы знаем AM, мы можем найти MR:

MR = 12 - AM = 12 - 9 = 3 см

Также, чтобы найти MB, мы можем воспользоваться фактом, что AB = AM + MB:

MB = AB - AM = 24 - 9 = 15 см

Ответ:

AM = 9 см
MR = 3 см
MB = 15 см

Answer 2

Given information:

- Length of segment AB = 24 cm. - Point M lies on segment AR. - AM is 3 times longer than segment MR.

Finding AM, MR, and MV:

To find the lengths of AM, MR, and MV, we can use the following steps:

Step 1: Find the length of MR. Since AM is 3 times longer than MR, we can set up the equation: AM = 3 * MR. We know that AB = AM + MR + MV. Substituting the value of AM from the equation above, we get: 24 = 3 * MR + MR + MV. Simplifying the equation, we have: 24 = 4 * MR + MV.

Step 2: Find the length of MV. We know that AB = 24 cm, and we can substitute the value of MR from the equation above to get: 24 = 4 * MR + MV. Since AB = AM + MR + MV, we can rewrite the equation as: 24 = 3 * MR + MR + MV + MV. Simplifying further, we have: 24 = 4 * MR + 2 * MV.

Step 3: Solve for MR and MV. We now have two equations: Equation 1: 24 = 4 * MR + MV Equation 2: 24 = 4 * MR + 2 * MV

Subtracting Equation 1 from Equation 2, we get: 0 = MV. This means that MV is equal to 0.

Substituting the value of MV = 0 into Equation 1, we get: 24 = 4 * MR + 0. Simplifying, we find that MR = 6 cm.

Step 4: Find the lengths of AM and MV. Since AM = 3 * MR, we can substitute the value of MR = 6 cm to get: AM = 3 * 6 = 18 cm.

Since MV = 0, the length of MV is 0 cm.

Therefore, the lengths of AM, MR, and MV are: - AM = 18 cm - MR = 6 cm - MV = 0 cm.

Please let me know if I can help you with anything else.