Question

Сколько можно составить различных прямоугольников площадью 42см2, если длины сторон этих прямоугольников являются натуральными числами ( прямоугольники со сторонами например 3 см, 4 см и 4 см, 3 см считаются одинаковыми)?

Answer 1

1*42=42 см2
2*21=42 см2
3*14=42 см2
6*7=42 см2
можно составить 4 прямоугольника со сторонами: 1см и 42см, 2см и 21см, 3см и 14см, 6см и 7см

Answer 2

Calculating the Number of Different Rectangles with an Area of 42 cm²

To calculate the number of different rectangles with an area of 42 cm², we can use the formula for the area of a rectangle: area = length × width. Given that the lengths of the sides are natural numbers, we need to find all the combinations of natural numbers that multiply to give an area of 42 cm².

Calculation Process

To find all the different rectangles, we can factorize the number 42 and then find all the combinations of factors that can form pairs of sides for the rectangles.

The factors of 42 are: - 1, 2, 3, 6, 7, 14, 21, 42

Now, we can pair these factors to find the different rectangles.

Result

The different rectangles with an area of 42 cm², considering the lengths of the sides as natural numbers, are as follows: 1. 1 cm × 42 cm 2. 2 cm × 21 cm 3. 3 cm × 14 cm 4. 6 cm × 7 cm

Therefore, there are 4 different rectangles that can be formed with an area of 42 cm², where the lengths of the sides are natural numbers.