Question

Знайдіть сторони трикутника, якщо вони відносяться як 1:2:3, а периметр дорівнює 18 см

Answer 1

Пусть меньшая сторона х, тогда из условия задачи можно записать
x+2x+3x=18 ⇒ 6x=18 ⇒ x=3 см; 2x=2*3=6 см; 3x=3*3=9 см.

Answer 2

Finding the Sides of a Triangle

To find the lengths of the sides of a triangle when they are in the ratio 1:2:3 and the perimeter is 18 cm, we can use the following steps:

1. Let's assume the lengths of the sides are x, 2x, and 3x, respectively, where x is a common factor.

2. The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is given as 18 cm. So, we can set up the equation:

x + 2x + 3x = 18

3. Simplifying the equation, we have:

6x = 18

4. Dividing both sides of the equation by 6, we find:

x = 3

5. Now that we have the value of x, we can find the lengths of the sides:

- The first side is x = 3 cm. - The second side is 2x = 2 * 3 = 6 cm. - The third side is 3x = 3 * 3 = 9 cm.

Therefore, the lengths of the sides of the triangle are 3 cm, 6 cm, and 9 cm, respectively.

Note: The lengths of the sides of a triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the lengths of the sides (3 cm, 6 cm, and 9 cm) satisfy this condition.