Question

сторони трикутника дорівнюють 6 см. 9 см. 12 см. знайти периметер подібного цьому трикутника якщо найменша і найбільша сторона цього дорівнює 9 см.​

Answer 1

Ответ:

Объяснение:

З умови, сторони трикутника відносяться, як 1 : 1.5 : 2.

Таким же є відношення сторін подібного йому трикутника.

Отже, найбільша і найменша сторони відносяться, як 1:2.

Найменша сторона дорівнює: 9 ÷ 3 =3 см

Найбільша дорівнює: 3 × 2 = 6 см

Середня сторона: 3 × 1.5 = 4.5 см

Р = 3 см + 6 см + 4.5 см = 13,5 см

Answer 2

Finding the Perimeter of a Similar Triangle

To find the perimeter of a similar triangle, we need to determine the ratio of similarity between the given triangle and the similar triangle. In this case, we are given a triangle with side lengths of 6 cm, 9 cm, and 12 cm, and we need to find the perimeter of a similar triangle with the smallest and largest sides measuring 9 cm.

Let's denote the sides of the given triangle as a, b, and c, with a being the smallest side and c being the largest side. We are given that a = 6 cm, b = 9 cm, and c = 12 cm.

We are also given that the smallest and largest sides of the similar triangle are 9 cm. Let's denote the sides of the similar triangle as x, y, and z, with x being the smallest side and z being the largest side. We need to find the perimeter of this similar triangle.

To find the ratio of similarity between the two triangles, we can divide the corresponding sides of the similar triangle by the corresponding sides of the given triangle. In this case, we can divide x by a and z by c:

x / a = 9 / 6 and z / c = 9 / 12.

Simplifying these ratios, we get:

x / 6 = 9 / 6 and z / 12 = 9 / 12.

Solving for x and z, we find:

x = (9 / 6) * 6 = 9 cm and z = (9 / 12) * 12 = 9 cm.

Therefore, the sides of the similar triangle are x = 9 cm, y = 9 cm, and z = 9 cm.

To find the perimeter of the similar triangle, we add up the lengths of all three sides:

Perimeter = x + y + z = 9 cm + 9 cm + 9 cm = 27 cm.

Therefore, the perimeter of the similar triangle is 27 cm.

Please note that the given information did not provide enough details to determine the exact shape of the triangle or the specific type of similarity (e.g., scale factor). The solution assumes that the sides of the similar triangle are proportional to the sides of the given triangle.