Question

Квадратную коробку заполнили в два слоя одинаковыми квадратными шоколадками. Кирилл съел все 20 шоколадок верхнего слоя, которые лежали вдоль стенок коробки. Сколько шоколадок осталось в коробке?

Answer 1

36*2=72 (

72-20=52 (потому что мальчик съел 20 конфет)

Answer 2

20 шоколадок по периметру это квадрат 6*6=36

в 1 слое 36

в 2 слоях 72

72-20=52 осталось

Answer 3

Problem Analysis

We have a square box filled with two layers of identical square chocolates. Kirill ate all 20 chocolates from the top layer that were along the walls of the box. We need to determine how many chocolates are left in the box.

Solution

To find the number of chocolates left in the box, we need to calculate the total number of chocolates in the box and subtract the number of chocolates Kirill ate.

Let's assume that there are 'n' chocolates in each row of the top layer. Since the box is square, there are 'n' chocolates in each column as well. Therefore, the total number of chocolates in the top layer is n * n = n^2.

Since there are two layers, the total number of chocolates in the box is 2 * (n^2) = 2n^2.

Kirill ate all 20 chocolates from the top layer, which means he ate n chocolates from each side of the box. Therefore, the number of chocolates Kirill ate is 4n.

To find the number of chocolates left in the box, we subtract the number of chocolates Kirill ate from the total number of chocolates in the box: 2n^2 - 4n.

Now we need to solve the equation 2n^2 - 4n = 20 to find the value of 'n'.

Calculation

Let's solve the equation 2n^2 - 4n = 20 to find the value of 'n'.

2n^2 - 4n - 20 = 0

Dividing the equation by 2:

n^2 - 2n - 10 = 0

Using the quadratic formula:

n = (-b ± √(b^2 - 4ac)) / (2a)

a = 1, b = -2, c = -10

n = (-(-2) ± √((-2)^2 - 4 * 1 * -10)) / (2 * 1)

n = (2 ± √(4 + 40)) / 2

n = (2 ± √44) / 2

n = (2 ± 2√11) / 2

n = 1 ± √11

Since the number of chocolates cannot be negative, we take the positive value:

n = 1 + √11

Therefore, the number of chocolates left in the box is 2n^2 - 4n = 2(1 + √11)^2 - 4(1 + √11).

Answer

The number of chocolates left in the box is 2(1 + √11)^2 - 4(1 + √11).