Question

Периметр прямоугольной детской площадки составляет 28 м. Какие размеры она должна иметь, чтобы площадь её была наибольшей?

Answer 1

Хз как объяснить но вроде вот

Answer 2

Finding the Dimensions of the Rectangular Playground

To find the dimensions of a rectangular playground with the maximum area, given that its perimeter is 28 meters, we can use the following steps:

1. Let's assume the length of the playground is L and the width is W. 2. The perimeter of a rectangle is given by the formula: Perimeter = 2L + 2W. 3. According to the given information, the perimeter is 28 meters. Therefore, we have the equation: 2L + 2W = 28.

Now, let's solve this equation to find the dimensions of the playground.

Solving the Equation

To solve the equation 2L + 2W = 28, we can rearrange it to isolate one variable and substitute it back into the equation to find the other variable.

1. Let's solve for L in terms of W: - Subtract 2W from both sides of the equation: 2L = 28 - 2W. - Divide both sides by 2: L = (28 - 2W) / 2.

2. Now, substitute the value of L in terms of W back into the equation 2L + 2W = 28: - Replace L with (28 - 2W) / 2: 2((28 - 2W) / 2) + 2W = 28. - Simplify the equation: 28 - 2W + 2W = 28. - The 2W terms cancel out, leaving us with 28 = 28.

Conclusion

The equation 2L + 2W = 28 simplifies to 28 = 28, which means that any values of L and W that satisfy this equation will give us a perimeter of 28 meters.

Therefore, there are infinitely many possible dimensions for the rectangular playground that would result in a perimeter of 28 meters. The specific dimensions will depend on the values chosen for L and W.

Please note that the question asks for the dimensions that would result in the maximum area. However, the given information does not provide any constraints or requirements for the aspect ratio or any other factors that would allow us to determine the dimensions that maximize the area.