Question

Длина прямоугольника на 5 см больше ширины и на 5 дм меньше периметра прямоугольника. Какова длина прямоугольника (в дециметрах)?

Answer 1

Ответ:

а = 2дм

Пошаговое объяснение:

а  (см) - длина прямоугольника

а - 5 (см) - ширина прямоугольника

2(а + а - 5) = 4а - 10 (см)- периметр прямоугольника

5дм = 50см

4а - 10  - а = 50 (см)

3а - 10 = 50

3а = 60

а = 20 (см) = 2 дм

Answer 2

Calculating the Length of the Rectangle

To find the length of the rectangle in decimeters, we can use the information provided in the question. Let's denote the width of the rectangle as x decimeters. According to the given information, the length of the rectangle is 5 centimeters more than the width, which can be expressed as (x + 0.5) decimeters. Additionally, the length is 5 decimeters less than the perimeter of the rectangle.

Setting Up the Equation

The perimeter of a rectangle is given by the formula: 2 * (length + width). Using this, we can set up the equation based on the given information: 2 * ((x + 0.5) + x) = 2x + 1 + 2x = 4x + 1

According to the given information, the length is 5 decimeters less than the perimeter, so we have: 4x - 5 = x + 0.5

Solving for x

Now, we can solve for x to find the width of the rectangle: 4x - 5 = x + 0.5 4x - x = 0.5 + 5 3x = 5.5 x = 5.5 / 3 x = 1.83 (rounded to two decimal places)

Calculating the Length

The length of the rectangle is 5 centimeters more than the width, which is (1.83 + 0.5) decimeters. Therefore, the length of the rectangle is approximately 2.33 decimeters.

So, the length of the rectangle in decimeters is approximately 2.33 decimeters.