Question

Стороны прямоугольника относятся как 2:3. Найдите их,если площадь прямоугольника равна 405 см в квадрате

Answer 1

Стороны равны - 18 и 27 соответственно.
18*27 = 486.
Подробно:
Составляем уравнение: 
Пусть 2x - первая сторона, а 3x - вторая, тогда:
 - не подходит, т.к. длина не может быть отрицательной.
 - первая сторона.
 - вторая сторона.

Answer 2

Finding the sides of a rectangle with a given area and a ratio of 2:3

To find the sides of a rectangle when the area and the ratio of the sides are given, we can follow these steps:

1. Let's assume the length of the rectangle is 2x and the width is 3x. Since the ratio of the sides is given as 2:3, we can express the length as 2x and the width as 3x.

2. The formula for the area of a rectangle is length x width. In this case, the area is given as 405 cm². So we can set up the equation:

2x * 3x = 405

3. Simplifying the equation, we get:

6x² = 405

4. To solve for x, we divide both sides of the equation by 6:

x² = 67.5

5. Taking the square root of both sides, we find:

x ≈ 8.21

6. Now that we have the value of x, we can find the length and width of the rectangle:

Length = 2x ≈ 2 * 8.21 ≈ 16.42 cm

Width = 3x ≈ 3 * 8.21 ≈ 24.63 cm

Therefore, the sides of the rectangle are approximately 16.42 cm and 24.63 cm, with a ratio of 2:3.