Question

Две стороны некоторого треугольника относятся как 3:5, а периметр этого треугольника - в четыре раза больше наименьшей стороны, длина которой 24 см. Найди стороны этого треугольника. Рассмотри все возможные варианты. Решение объясни.

Answer 1

Не знаю, какое объяснение хотят увидеть, но я решила так.

Answer 2

Problem Analysis

We are given that the ratio of two sides of a triangle is 3:5, and the perimeter of the triangle is four times the length of the smallest side, which is 24 cm. We need to find the lengths of all three sides of the triangle.

Solution

Let's assume the lengths of the two sides of the triangle are 3x and 5x, where x is a common factor. We can find the perimeter of the triangle by adding the lengths of all three sides:

Perimeter = 3x + 5x + 24 cm

According to the problem, the perimeter is four times the length of the smallest side, which is 24 cm:

4 * 24 cm = 3x + 5x + 24 cm

Simplifying the equation:

96 cm = 8x + 24 cm

Subtracting 24 cm from both sides:

72 cm = 8x

Dividing both sides by 8:

9 cm = x

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

Smallest side = 3x = 3 * 9 cm = 27 cm Largest side = 5x = 5 * 9 cm = 45 cm

Therefore, the lengths of the sides of the triangle are 27 cm, 45 cm, and the third side can be any length that satisfies the given ratio.

Answer

The lengths of the sides of the triangle are 27 cm and 45 cm. The length of the third side can be any length that satisfies the given ratio of 3:5.