Question

Паша вырезал из бумаги несколько пятиугольников и шестиугольников.Всего у вырезанных фигурок 32 вершины.Сколько шестиугольников вырезал Паша? Я знаю ответ,но я не понимаю.Почему другие пишут про пятиугольники,хотя сказано найти только шестиугольники! Ответьте пожалуйста, срочно!​

Answer 1

Ответ:

2 шестиугольника

Пошаговое объяснение:

если взять 4 пятиугольника (5*4=20)

и 2 шестиугольника (6*2=12)

решение получается: 20+12=32

Answer 2

Problem Analysis

Pasha has cut out several pentagons and hexagons from paper. The total number of vertices in the cut-out shapes is 32. We need to determine how many hexagons Pasha cut out.

Solution

Let's assume that Pasha cut out x hexagons and y pentagons.

Each hexagon has 6 vertices, so the total number of vertices in the hexagons is 6x. Similarly, each pentagon has 5 vertices, so the total number of vertices in the pentagons is 5y.

According to the problem, the total number of vertices in the cut-out shapes is 32. Therefore, we can write the following equation:

6x + 5y = 32

We need to find the value of x, which represents the number of hexagons.

To solve this equation, we can use trial and error or substitution. Let's use trial and error to find the solution.

Trial and Error

Let's start by assuming that Pasha cut out 1 hexagon (x = 1). In this case, the equation becomes:

6(1) + 5y = 32 6 + 5y = 32 5y = 32 - 6 5y = 26 y = 26/5 = 5.2

Since the number of pentagons cannot be a decimal, this assumption is incorrect.

Let's try assuming that Pasha cut out 2 hexagons (x = 2). In this case, the equation becomes:

6(2) + 5y = 32 12 + 5y = 32 5y = 32 - 12 5y = 20 y = 20/5 = 4

This assumption satisfies the condition that the number of pentagons is a whole number. Therefore, Pasha cut out 2 hexagons and 4 pentagons.

Answer

Pasha cut out 2 hexagons.

Explanation

The problem states that Pasha cut out several pentagons and hexagons. However, it does not specify the exact number of each shape. Therefore, we need to consider both pentagons and hexagons in our solution.

Other people may mention pentagons in their explanations because the problem mentions that Pasha cut out both pentagons and hexagons. However, the focus of the question is to determine the number of hexagons, so we prioritize finding the number of hexagons in our solution.

Please let me know if you need any further clarification.