Question

Знайдіть сторони трикутника, якщо вони пропорційні числам 3, 5 і 7, а периметр трикутника дорівнює 60 см.

Answer 1

Ответ:

Нехай X - коефіцієнт пропорційності, тоді:

3x+5x+7x=60

15x=60

X=4

Сторони трикутника:

12 см, 20 см, 28 см

Answer 2

Finding the Sides of a Proportional Triangle

To find the sides of a triangle when they are proportional to the numbers 3, 5, and 7, and the perimeter of the triangle is 60 cm, we can use the concept of proportionality.

Let's assume the sides of the triangle are represented by the variables x, y, and z. According to the given information, we have the following proportions:

x : y : z = 3 : 5 : 7

To find the actual values of x, y, and z, we need to determine the common ratio that relates the sides of the triangle. We can do this by dividing the perimeter of the triangle by the sum of the proportions:

x + y + z = 60 cm

Using the proportions, we can express x, y, and z in terms of the common ratio:

x = 3k y = 5k z = 7k

Substituting these values into the equation for the perimeter, we get:

3k + 5k + 7k = 60

Simplifying the equation, we have:

15k = 60

Dividing both sides of the equation by 15, we find:

k = 4

Now we can substitute the value of k back into the expressions for x, y, and z to find their actual values:

x = 3 * 4 = 12 cm y = 5 * 4 = 20 cm z = 7 * 4 = 28 cm

Therefore, the sides of the triangle are 12 cm, 20 cm, and 28 cm.

Note: The source provided does not contain relevant information for this specific question. The solution provided is based on mathematical principles and calculations.