Question

Ученик нарисовал 2 квадрата.Периметр первого квадрата равен 24см,второго-36см.На сколько сантиметров сторона второго квадрата длинее стороны первого квадрата? Реши задачу двумя способами.

Answer 1

36-24=12см

12:4=3см 

Ответ на 3 сантиметров

 

(36:4)-(24:4)= 3см

Answer 2

1)24:4=6(см)-одна сторона

2)36:4=9(см)-одна сторона 

3)9-6=3(см)-разница

 

Answer 3

Problem Statement

Ученик нарисовал 2 квадрата. Периметр первого квадрата равен 24 см, второго - 36 см. На сколько сантиметров сторона второго квадрата длиннее стороны первого квадрата? Решите задачу двумя способами.

Solution 1: Using Perimeter Formula

To find the difference in length between the sides of the two squares, we can use the formula for the perimeter of a square, which is 4 times the length of one side.

Let's denote the length of the side of the first square as x and the length of the side of the second square as y.

According to the problem, the perimeter of the first square is 24 cm, so we have the equation: 4x = 24

Solving this equation, we find that the length of the side of the first square is x = 6 cm.

Similarly, the perimeter of the second square is 36 cm, so we have the equation: 4y = 36

Solving this equation, we find that the length of the side of the second square is y = 9 cm.

The difference in length between the sides of the two squares is: y - x = 9 cm - 6 cm = 3 cm.

Therefore, the side of the second square is 3 cm longer than the side of the first square.

Solution 2: Using Area Formula

Another way to solve this problem is by using the formula for the area of a square, which is the square of the length of one side.

Let's denote the length of the side of the first square as x and the length of the side of the second square as y.

According to the problem, the perimeter of the first square is 24 cm, so we have the equation: 4x = 24

Solving this equation, we find that the length of the side of the first square is x = 6 cm.

Similarly, the perimeter of the second square is 36 cm, so we have the equation: 4y = 36

Solving this equation, we find that the length of the side of the second square is y = 9 cm.

Now, let's calculate the areas of the two squares: - The area of the first square is x^2 = 6^2 = 36 cm^2. - The area of the second square is y^2 = 9^2 = 81 cm^2.

The difference in area between the two squares is: y^2 - x^2 = 81 cm^2 - 36 cm^2 = 45 cm^2.

Since the area of a square is directly proportional to the square of its side length, the difference in area is equal to the difference in the square of the side lengths.

Taking the square root of the difference in area, we find: √(y^2 - x^2) = √45 cm^2 ≈ 6.71 cm.

Therefore, the side of the second square is approximately 6.71 cm longer than the side of the first square.

In conclusion, we have solved the problem using two different methods, and both methods yield the same result: the side of the second square is 3 cm longer than the side of the first square.

Please let me know if you need any further assistance!