Question

В противоположных углах квадратной комнаты расстелили два одинаковых прямоугольных ковра, каждый из которых двумя своими сторонами примыкает к стенам комнаты. Площадь, накрытая одновременно обоими коврами, оказалась равной 13 м2. Затем из ковров развернули в своем углу на 90º. После этого площадь, накрытая одновременно обоими коврами, оказалась 9 м2. На сколько метров длина ковра больше его ширины?

Answer 1

Ответ : 2 1/2 13 делем 2 - 4 делем 2 =2 1/2

Answer 2

Problem Analysis

We have a square room with two identical rectangular carpets placed in opposite corners of the room. The area covered by both carpets together is initially 13 square meters. After rotating the carpets by 90 degrees, the area covered by both carpets is reduced to 9 square meters. We need to find the difference between the length and width of the carpet.

Solution

Let's assume the length of the carpet is L and the width is W.

1. Initially, the area covered by both carpets is 13 square meters. This can be represented by the equation: 2LW = 13.

2. After rotating the carpets by 90 degrees, the area covered by both carpets is reduced to 9 square meters. This can be represented by the equation: 2WL = 9.

To find the difference between the length and width of the carpet, we need to solve these two equations simultaneously.

Solving the Equations

Let's solve the equations using substitution:

From equation 1, we can express L in terms of W: L = 13 / (2W).

Substituting this value of L into equation 2, we get: 2W * (13 / (2W)) = 9.

Simplifying the equation, we have: 13 = 9.

This equation is not possible to solve, as it leads to a contradiction. Therefore, there is no solution to this problem.

Conclusion

Based on the given information, there is no solution to the problem. The equations derived from the problem lead to a contradiction, indicating that the problem is not solvable.