Question

Длина прямоугольника на 8 см больше стороны квадрата , а ширина - на 8 см меньше . У какой из фигур площадь больше и на сколько ? Решите срочно пожалуйста ..

Answer 1

Х- сторона квадрата
Площадь квадрата -х²
Длина прямоугольника х+8
Ширина                         х-8
Площадь (х-8)(х+8)

Разница между площадями: х²-(х-8)(х+8)=х²-(х²-64)=х²-х²-64=64 (см²)

Answer 2

Problem Analysis

We are given that the length of a rectangle is 8 cm longer than the side of a square, and the width of the rectangle is 8 cm shorter than the side of the square. We need to determine which figure has a larger area and by how much.

Solution

Let's assume the side length of the square is x cm.

According to the given information, the length of the rectangle is 8 cm longer than the side of the square, so the length of the rectangle is x + 8 cm.

Similarly, the width of the rectangle is 8 cm shorter than the side of the square, so the width of the rectangle is x - 8 cm.

The area of the square is given by x^2 square cm.

The area of the rectangle is given by length × width, which is (x + 8) × (x - 8) square cm.

To determine which figure has a larger area, we need to compare the area of the square and the area of the rectangle.

Comparing the Areas

To compare the areas, we can subtract the area of the square from the area of the rectangle:

Area of Rectangle - Area of Square = (x + 8) × (x - 8) - x^2

Simplifying the expression:

Area of Rectangle - Area of Square = x^2 - 64

Now, we need to determine the value of x that makes the expression x^2 - 64 positive.

Finding the Value of x

To find the value of x, we can set the expression x^2 - 64 greater than zero:

x^2 - 64 > 0

Solving this inequality, we find:

x > 8 or x < -8

Since the side length of a square cannot be negative, we can conclude that x > 8.

Therefore, the side length of the square must be greater than 8 cm.

Conclusion

Based on the analysis, we can conclude that the area of the rectangle is larger than the area of the square. However, without knowing the specific value of x, we cannot determine the exact difference in their areas.

Please let me know if you need any further clarification or assistance!