Question

Маша помнит, что периметр прямоугольной формы торта равен 30 см. Сколько существует вариантов различных прямоугольных форм, если длина сторон выражены целым числом сантиметров и каждая сторона не меньше 3 см

Answer 1

Ответ:

Һгиниһнинрүрұрұргррг

Answer 2

Number of Different Rectangular Cake Shapes

To find the number of different rectangular cake shapes with integer side lengths, we need to consider the given conditions: the perimeter of the cake is 30 cm, and each side must be at least 3 cm.

Let's break down the problem step by step:

1. Determine the possible range of side lengths: - Since each side must be at least 3 cm, the minimum side length is 3 cm. - The maximum side length can be found by dividing the perimeter by 2, as the sum of the lengths of opposite sides of a rectangle is equal to the perimeter. - Therefore, the maximum side length is 30/2 = 15 cm.

2. Calculate the number of possible side lengths: - We need to find the number of integers between 3 and 15 (inclusive). - The range of integers is 3, 4, 5, ..., 15. - To find the count of integers in this range, we subtract the starting value from the ending value and add 1. - So, the number of possible side lengths is 15 - 3 + 1 = 13.

3. Calculate the number of different rectangular cake shapes: - Since we have 13 possible side lengths, we can choose any two side lengths to form a rectangle. - The number of ways to choose two side lengths from 13 is given by the combination formula: C(13, 2) = 13! / (2! * (13-2)!) = 13! / (2! * 11!) = (13 * 12) / (2 * 1) = 78.

Therefore, there are 78 different rectangular cake shapes that satisfy the given conditions.