Question

Ширину прямоугольника увеличили на 5 см и получили квадрат, площадь которого больше площади прямоугольника на 40 см"во второй степени".

Answer 1

Пусть х см-сторона квадрата,длина прямоугольника, тогда ширина прямоугольника 5х.
Составим уравнение.
х:2-х*(х-5)=40
5х=40
х=8
 Х-5=8-5=3 см ширина прямоугольника

8*3=24 см:2 площадь прямоугольника

Answer 2

Problem Analysis

We are given that the width of a rectangle is increased by 5 cm, resulting in a square with an area that is 40 square cm larger than the area of the rectangle. We need to find the original width of the rectangle.

Solution

Let's assume the original width of the rectangle is x cm. After increasing the width by 5 cm, the new width becomes x + 5 cm. Since the resulting shape is a square, the length of the square is also x + 5 cm.

The area of the rectangle is given by the formula: Area = length × width. Therefore, the area of the rectangle is x × (x + 5) square cm.

The area of the square is given by the formula: Area = side × side. Therefore, the area of the square is (x + 5) × (x + 5) square cm.

According to the problem, the area of the square is 40 square cm larger than the area of the rectangle. So we can set up the following equation:

(x + 5) × (x + 5) = x × (x + 5) + 40

Now, let's solve this equation to find the value of x.

Expanding the equation:

x^2 + 10x + 25 = x^2 + 5x + 40

Simplifying the equation:

x^2 + 10x + 25 - x^2 - 5x - 40 = 0

Combining like terms:

5x - 15 = 0

Simplifying further:

5x = 15

Dividing both sides by 5:

x = 3

Therefore, the original width of the rectangle is 3 cm.

Answer

The original width of the rectangle is 3 cm.