Question

Два участка земли имеют одинаковую площадь. Один из них квадрат со стороной 10 м, а другой прямоугольник длина которого равна 20 м. Оба участка обнесли изгородью. У какого участка изгородь длиннее? На сколько?

Answer 1

Problem Analysis

We are given two plots of land with the same area. One plot is a square with a side length of 10 meters, and the other plot is a rectangle with a length of 20 meters. We need to determine which plot has a longer perimeter and by how much.

Solution

To find the perimeter of a square, we multiply the length of one side by 4. Therefore, the perimeter of the square plot is 4 * 10 = 40 meters.

To find the perimeter of a rectangle, we add the lengths of all four sides. In this case, the length of the rectangle is given as 20 meters, but we are not given the width. However, since the area of the rectangle is the same as the area of the square, we can calculate the width of the rectangle using the formula for the area of a rectangle: area = length * width.

Since the area of the rectangle is the same as the area of the square, we have:

10 * width = 10 * 10

Simplifying the equation, we find:

width = 10 meters

Now we can calculate the perimeter of the rectangle. The length is given as 20 meters, and the width is 10 meters. Therefore, the perimeter of the rectangle is 2 * (20 + 10) = 60 meters.

Comparing the perimeters, we can see that the rectangle has a longer perimeter than the square. The difference in perimeter lengths is 60 - 40 = 20 meters.

Therefore, the rectangle's fence is 20 meters longer than the square's fence.

Conclusion

The plot of land in the shape of a rectangle, with a length of 20 meters, has a longer fence than the square plot, with a side length of 10 meters. The difference in fence lengths is 20 meters.