Question

Трикутники АВС і MNK подібні. АВ=2см, ВС=4см, АС=5см, МК=10см. Знайти периметр трикутника MNK

Answer 1

РУССКИЙ
Решение:
1) ΔABC ~ ΔMNK (По условию)
Pabc = AB + BC + AC = 2 + 5 + 4 = 11 см
2) Из подобия треугольников следует, что $\frac{MN}{AB} = \frac{NK}{BC} = \frac{MK}{AC} = k$
k = 5
Pmnk = k * Pabc = 5 * 11 = 55 см, так как периметры подобных треугольников относятся как коэффициент подобия.
Ответ: 55 см

УКРАЇНСЬКИЙ
Рішення:
1) ΔABC ~ ΔMNK (За умовою)
Pabc = AB + BC + AC = 2 + 5 + 4 = 11 см
2) З подоби трикутників випливає, що $\frac{MN}{AB} = \frac{NK}{BC} = \frac{MK}{AC} = k$
k = 5
Pmnk = k * Pabc = 5 * 11 = 55 см, так як периметри подібних трикутників відносяться як коефіцієнт подібності.
Відповідь: 55 см

Answer 2

Given Information:

We are given that triangles ABC and MNK are similar. We also know the following measurements: - AB = 2 cm - BC = 4 cm - AC = 5 cm - MK = 10 cm

Finding the Perimeter of Triangle MNK:

To find the perimeter of triangle MNK, we need to determine the lengths of its sides. Since triangles ABC and MNK are similar, their corresponding sides are proportional.

Let's denote the length of side MN as x. Since AB is 2 cm and MK is 10 cm, we can set up the following proportion:

AB/MK = BC/NK

Substituting the given values, we have:

2/10 = 4/x

Simplifying the equation, we get:

2x = 40

Dividing both sides by 2, we find:

x = 20

Therefore, the length of side MN is 20 cm.

Now, we can calculate the perimeter of triangle MNK by adding the lengths of its sides:

Perimeter of MNK = MN + NK + MK = 20 cm + 4 cm + 10 cm = 34 cm

Hence, the perimeter of triangle MNK is 34 cm.

Conclusion:

The perimeter of triangle MNK is 34 cm, given that triangles ABC and MNK are similar and the lengths of AB, BC, AC, and MK are known.