Question

Периметр равностороннего треугольника 18 см. На его сторонах во внешнюю сторону построены равные равнобедренные треугольники, сумма периметров которых 60 см. Найти стороны этих равнобедренных треугольников. только прошу подробно расписать, пожалуйста

Answer 1

Ответ:

a = b = 7 см, c = 6 см

Объяснение:

Сторона равностороннего треугольника x

P∆ = 3x

x = P∆/3 = 18/3 = 6 см

P1, P2, P3 - периметры равнобедренных треугольников

Так как P1 = P2 = P3, приравняем их к P

P1 + P2 + P3 = 3P = 60 см

P = 60/3 = 20 см

a, b - боковые стороны равнобедренных треугольников

с - основа, которая равна сторонее равностороннего треугольника - 6 см

Так как a = b, то a+b+c = a+a+c = 20 см

2a + 6 = 20

2a = 20 - 6 = 14

a = 14/2 = 7 см

Проверим: 6 равных сторон (по 2 каждому теугольнику) и три равных основания (по одному) должны дать в сумме 60

6*7 + 3*6 = 42 + 18 = 60 см (всё правильно)

Answer 2

Problem Analysis

We are given an equilateral triangle with a perimeter of 18 cm. On each side of this triangle, equal isosceles triangles are constructed on the outer side. The sum of the perimeters of these isosceles triangles is 60 cm. We need to find the lengths of the sides of these isosceles triangles.

Solution

Let's denote the length of each side of the equilateral triangle as x cm. Since it is an equilateral triangle, all sides are equal.

The perimeter of an equilateral triangle is given by the formula: Perimeter = 3 * side length.

Given that the perimeter of the equilateral triangle is 18 cm, we can write the equation:

18 = 3x

Simplifying the equation, we find:

x = 6 cm

Now, let's denote the length of each leg of the isosceles triangles as y cm. Since the isosceles triangles are constructed on the outer side of the equilateral triangle, their bases are equal to the sides of the equilateral triangle.

The perimeter of an isosceles triangle is given by the formula: Perimeter = 2 * base length + leg length.

Given that the sum of the perimeters of the isosceles triangles is 60 cm, we can write the equation:

60 = 2x + 2y

Substituting the value of x from the previous equation, we have:

60 = 2 * 6 + 2y

Simplifying the equation, we find:

60 = 12 + 2y

2y = 60 - 12

2y = 48

y = 24 cm

Therefore, the length of each leg of the isosceles triangles is 24 cm.

To summarize: - The length of each side of the equilateral triangle is 6 cm. - The length of each leg of the isosceles triangles is 24 cm.

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