Question

Стороны треугольника пропорциональны числам 3,4,5,а его периметр равен 36 см. Найдите длины сторон.

Answer 1

Обозначим за х - коэффициент пропорциональности, тогда стороны равны 3x;4x;5x. Периметр треугольника равен сумме всех сторон.

3x+4x+5x = 12x.

12x = 36

x = 3

Стороны треугольника: 9; 12; 15.

Answer 2

To find the lengths of the sides of the triangle, we first need to determine the value of 'a' and then use the given proportions (3, 4, 5) to calculate the lengths of the sides.

Let's proceed step-by-step:

Step 1: Find the value of 'a' Since the perimeter of the triangle is 36 cm, we can set up the equation:

3 + 4 + 5 + a = 36

Step 2: Solve for 'a' a = 36 - (3 + 4 + 5) a = 36 - 12 a = 24

Now that we have the value of 'a' (which is 24), we can use the given proportions (3, 4, 5) to find the lengths of the sides of the triangle.

Step 3: Calculate the lengths of the sides using the proportions: The sides of the triangle are proportional to 3, 4, and 5, so we can find their lengths by multiplying each proportion by a common factor. Let's use the common factor k:

Side 1: 3 * k Side 2: 4 * k Side 3: 5 * k

Step 4: Find the value of k: To find the value of k, we'll use the fact that the perimeter of the triangle is the sum of all three sides:

3 * k + 4 * k + 5 * k + 24 = 36

Step 5: Solve for k: 12 * k + 24 = 36

Subtract 24 from both sides:

12 * k = 12

Now, divide both sides by 12 to find the value of k:

k = 1

Step 6: Calculate the lengths of the sides using k:

Side 1: 3 * 1 = 3 cm Side 2: 4 * 1 = 4 cm Side 3: 5 * 1 = 5 cm

So, the lengths of the sides of the triangle are 3 cm, 4 cm, and 5 cm.