Question

Тимофей огородил два загона для коз. Оказалось, что для каждого загона понадобилось одинаковое количество метров ограждения. Первый загон прямоугольный со сторонами 180 м и 160 м, а второй — квадратный. Какой загон имеет большую площадь? Загон прямоугольной формы Загон квадратной формы На сколько квадратных метров больше?

Answer 1

Ответ:

Второй загон, квадратный, со стороной 170 м.

S1 = 180 * 160 = 28800 м^2 - прямоугольный

S2 = 170 * 170 = 28900 м^2 - квадратный

Получается, что площадь квадратного загона больше площади прямоугольного на 100 квадратных метров.

Answer 2

Problem Analysis

To determine which enclosure has a larger area, we need to calculate the areas of both enclosures and compare them. The first enclosure is rectangular, with sides measuring 180 m and 160 m. The second enclosure is square, so all sides are equal in length. We need to find the difference in area between the two enclosures.

Calculation

Let's calculate the areas of both enclosures and find the difference.

The area of a rectangle is given by the formula: Area = length × width. The area of a square is given by the formula: Area = side × side.

For the first enclosure (rectangular): - Length = 180 m - Width = 160 m

For the second enclosure (square): - Side = ?

Solution

To find the side length of the square enclosure, we can use the fact that both enclosures require the same amount of fencing. The perimeter of a rectangle is given by the formula: Perimeter = 2 × (length + width). Since the amount of fencing required is the same for both enclosures, we can set up the following equation:

2 × (180 + 160) = 4 × side

Simplifying the equation: 340 = 4 × side

Dividing both sides by 4: side = 340 / 4 = 85 m

Now that we have the side length of the square enclosure, we can calculate the areas of both enclosures.

For the first enclosure (rectangular): - Length = 180 m - Width = 160 m

Area = 180 × 160 = 28,800 square meters

For the second enclosure (square): - Side = 85 m

Area = 85 × 85 = 7,225 square meters

Answer

The rectangular enclosure has a larger area than the square enclosure. The difference in area is given by:

28,800 - 7,225 = 21,575 square meters

Therefore, the rectangular enclosure has an area that is 21,575 square meters larger than the square enclosure.