Question

Стороны прямоугольного листа бумаги имеют целочисленную длину ( в сантиметрах), а площадь листа равна 12 см2. Сколько квадратов площадью 4 см2 можно вырезать из этого прямоугольника?

Answer 1

Прямоугольный лист, и его площадь равна 12 см^2
Чтобы узнать, какое количество получится квадратов при вырезании, нужно 12:4 = 3 шт
Ответ:3

Answer 2

Calculation of the Number of Squares that can be Cut from a Rectangular Sheet of Paper

To determine the number of squares with an area of 4 cm² that can be cut from a rectangular sheet of paper with integer side lengths and a total area of 12 cm², we can follow these steps:

1. Find the possible dimensions of the rectangular sheet of paper that satisfy the given conditions. 2. Calculate the number of squares that can be cut from the rectangular sheet.

Step 1: Finding the Possible Dimensions of the Rectangular Sheet

Given that the rectangular sheet of paper has a total area of 12 cm², we need to find two side lengths that multiply to give 12. Since the side lengths are integers, we can consider all possible pairs of integers whose product is 12.

The possible pairs of side lengths for the rectangular sheet are: - (1 cm, 12 cm) - (2 cm, 6 cm) - (3 cm, 4 cm)

Step 2: Calculating the Number of Squares

Now that we have the possible dimensions of the rectangular sheet, we can calculate the number of squares with an area of 4 cm² that can be cut from each possible rectangular sheet.

For the rectangular sheet with side lengths (1 cm, 12 cm): - The longer side length (12 cm) is not divisible by 4, so no squares with an area of 4 cm² can be cut from this sheet.

For the rectangular sheet with side lengths (2 cm, 6 cm): - The longer side length (6 cm) is divisible by 4, so we can cut squares with an area of 4 cm² from this sheet. - The number of squares that can be cut is equal to the area of the rectangular sheet divided by the area of each square: 6 cm² / 4 cm² = 1.5 squares. - Since we cannot have a fraction of a square, we can only cut 1 square from this sheet.

For the rectangular sheet with side lengths (3 cm, 4 cm): - Both side lengths are divisible by 4, so we can cut squares with an area of 4 cm² from this sheet. - The number of squares that can be cut is equal to the area of the rectangular sheet divided by the area of each square: 12 cm² / 4 cm² = 3 squares.

Therefore, from the given rectangular sheet of paper with integer side lengths and a total area of 12 cm², we can cut a total of 4 squares with an area of 4 cm².

Please let me know if you need any further clarification or assistance!