Question

На плоту есть квадратный парус со стороной 9 дм. Смогут ли отважные путешественники накрыть этим парусом прямоугольную площадку в 72 дм квадратных и спасти от дождя свои припасы, если длина этой площадки 9 дм.? Сравните периметры паруса и площадки.

Answer 1

Смогут. Плошадь паруса=9*9=81Площадь площадки=72Размеры паруса 9 на 9=81Размеры площадки 9 на 8=72Так как площадь паруса больше и одна из сторон у них одинаковая, парус сможет полностью охватить площадку

Answer 2

Problem Analysis

The problem states that there is a square sail on a raft with a side length of 9 dm. The question is whether the brave travelers will be able to cover a rectangular platform with an area of 72 dm² using this sail, given that the length of the platform is 9 dm. We need to compare the perimeters of the sail and the platform to determine if the sail can cover the platform.

Solution

To determine if the sail can cover the platform, we need to compare the perimeters of the sail and the platform. If the perimeter of the sail is greater than or equal to the perimeter of the platform, then the sail can cover the platform.

Perimeter of the Sail

The sail is a square with a side length of 9 dm. The formula to calculate the perimeter of a square is P = 4s, where P is the perimeter and s is the side length. Substituting the given side length of 9 dm into the formula, we get:

P_sail = 4 * 9 dm = 36 dm

Perimeter of the Platform

The platform is a rectangle with a length of 9 dm and an unknown width. The formula to calculate the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width. Substituting the given length of 9 dm into the formula, we get:

P_platform = 2(9 dm + w) = 18 dm + 2w

Comparison

To determine if the sail can cover the platform, we need to compare the perimeters:

P_sail >= P_platform

Substituting the values we calculated:

36 dm >= 18 dm + 2w

Simplifying the inequality:

18 dm >= 2w

Dividing both sides by 2:

9 dm >= w

Conclusion

The inequality 9 dm >= w means that the width of the platform must be less than or equal to 9 dm for the sail to cover it. Since the length of the platform is also 9 dm, this means that the platform must be a square with sides of 9 dm or smaller for the sail to cover it.

Therefore, if the platform is a square with sides of 9 dm or smaller, the brave travelers will be able to cover it with the sail and protect their supplies from the rain.

Answer

Yes, the brave travelers will be able to cover the rectangular platform with an area of 72 dm² using the square sail with a side length of 9 dm, given that the length of the platform is also 9 dm. The sail can cover the platform if the platform is a square with sides of 9 dm or smaller.