Question

Из квадратной клумбы хотят сделать прямоугольную. Одну сторону клумбы хотят увеличить на 30 30 см, а вторую сторону уменьшить на 20 20 см. Найди изначальную сторону клумбы, если известно, что площадь новой клумбы стала больше на 30 30 см.

Answer 1

Ответ:

площадь прямоугольной клумбы S=20×30=60

площадь новой клумбы S=30×30=90²

сравниваем площади 90>60

следовательно площадь новой клумбы больше 60-90=30

Ответ: 30 изначальная сторона клумбы

Answer 2

Problem Analysis

We are given a square flower bed that needs to be transformed into a rectangular one. One side of the flower bed is to be increased by 30 cm, while the other side is to be decreased by 20 cm. We need to find the original side length of the flower bed, given that the area of the new flower bed is 30 cm² larger than the original.

Solution

Let's assume the original side length of the square flower bed is x cm. After the transformation, one side is increased by 30 cm, so the new length is x + 30 cm. The other side is decreased by 20 cm, so the new width is x - 20 cm.

The area of the original square flower bed is x * x = x² cm². The area of the new rectangular flower bed is (x + 30) * (x - 20) = x² + 10x - 600 cm².

According to the problem statement, the area of the new flower bed is 30 cm² larger than the original. Therefore, we can set up the following equation:

x² + 10x - 600 = x² + 30

Simplifying the equation, we get:

10x - 600 = 30

Adding 600 to both sides, we have:

10x = 630

Dividing both sides by 10, we get:

x = 63

Therefore, the original side length of the square flower bed is 63 cm.

Answer

The original side length of the square flower bed is 63 cm.