Question

Длина прямоугольника равна 12 дм это в 2 раза больше длины стороны квадрата ширина прямоугольника на 8 дм меньше его длины площадь Какой фигуры больше И на сколько квадратных дециметров больше?

Answer 1

12-8=4 дм - ширина прямоугольника
$S=a*b=12*4=48$ дм² - площадь прямоугольника
12:2=6 дм - сторона квадрата
$S=a*a=6*6=36$ дм² - площадь квадрата
48-36=12 дм² - разница в площади фигур
Ответ: площадь прямоугольника больше площади квадрата на 12 дм².

Answer 2

Problem Analysis

We are given the following information: - The length of a rectangle is 12 dm, which is twice the length of a side of a square. - The width of the rectangle is 8 dm less than its length.

We need to determine: 1. The shape with the greater area. 2. The difference in area between the two shapes.

Solution

To solve this problem, we can follow these steps: 1. Calculate the length of the side of the square. 2. Calculate the width of the rectangle. 3. Calculate the area of the square. 4. Calculate the area of the rectangle. 5. Compare the areas of the two shapes. 6. Calculate the difference in area between the two shapes.

Let's calculate each step in detail.

Step 1: Calculate the length of the side of the square

Given that the length of the rectangle is 12 dm, which is twice the length of a side of the square, we can calculate the length of the side of the square by dividing the length of the rectangle by 2.

Length of the side of the square = 12 dm / 2 = 6 dm.

Step 2: Calculate the width of the rectangle

Given that the width of the rectangle is 8 dm less than its length, we can calculate the width of the rectangle by subtracting 8 dm from the length of the rectangle.

Width of the rectangle = Length of the rectangle - 8 dm = 12 dm - 8 dm = 4 dm.

Step 3: Calculate the area of the square

The area of a square is calculated by multiplying the length of its side by itself.

Area of the square = (Length of the side of the square)^2 = (6 dm)^2 = 36 dm^2.

Step 4: Calculate the area of the rectangle

The area of a rectangle is calculated by multiplying its length by its width.

Area of the rectangle = Length of the rectangle * Width of the rectangle = 12 dm * 4 dm = 48 dm^2.

Step 5: Compare the areas of the two shapes

To determine which shape has a greater area, we compare the areas of the square and the rectangle.

The area of the rectangle (48 dm^2) is greater than the area of the square (36 dm^2).

Step 6: Calculate the difference in area between the two shapes

To calculate the difference in area between the two shapes, we subtract the area of the square from the area of the rectangle.

Difference in area = Area of the rectangle - Area of the square = 48 dm^2 - 36 dm^2 = 12 dm^2.

Therefore, the rectangle has a greater area than the square, and the difference in area between the two shapes is 12 square decimeters.