Question

В треугольнике MNPK сторона MN =x см выразите остальные стороны этого треугольника если: а)NP на 2 см меньше MN b)PK в 2 раза больше MNc)MP на 2 см больше PK 2)Зная что периметр MNPK равен 18 см используя данные пункта 1 составьте уравнение 3)Решите уравнение полученное в пункте 2 найдите длину MNПЖ СДЕЛАЙТЕ ЗА 6 МИНУТ​

Answer 1

Ответ:

1)

a) NP = x-2

b) PK = 2x

c) MP = 2x+2

2) x+(x-2)+2x+(2x+2) = 18

3x+(x-2)+(2x+2)=18

6x=18

x=3

3) MN=3 см

Пошаговое объяснение:

Answer 2

Finding the lengths of the sides of triangle MNPK

To find the lengths of the sides of triangle MNPK, we'll use the given information and solve for the unknown side lengths.

a) If NP is 2 cm less than MN: - Let NP = MN - 2 cm - The lengths of the sides are: MN = x cm, NP = (x - 2) cm, PK = ?

b) If PK is 2 times greater than MN: - Let PK = 2 * MN - The lengths of the sides are: MN = x cm, NP = ?, PK = 2x cm

c) If MP is 2 cm greater than PK: - Let MP = PK + 2 cm - The lengths of the sides are: MN = ?, NP = ?, PK = x cm, MP = (x + 2) cm

Writing the equation using the perimeter

Given that the perimeter of MNPK is 18 cm, we can write the equation using the side lengths obtained from the previous step.

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, we have:

MN + NP + PK + MP = 18 cm

Substituting the expressions for the side lengths obtained earlier, we get:

x + (x - 2) + 2x + (x + 2) = 18 cm

Simplifying the equation, we have:

5x = 18 cm

Solving the equation

To find the length of MN, we need to solve the equation:

5x = 18 cm

Dividing both sides of the equation by 5, we get:

x = 3.6 cm

Therefore, the length of MN is 3.6 cm.

Please note that the solution provided is based on the given information and assumptions made about the triangle MNPK.