Question

Площадь прямоугольника равна 900. каковы должны быть длинна и ширина этого прямоугольника чтобы его прериметр был наименьшим?

Answer 1

90 длина и 10 ширина
Р= 2*(90+10)= 200 

Answer 2

Calculating the Dimensions for the Rectangle

To find the dimensions of the rectangle that would result in the smallest perimeter while having an area of 900, we can use the formula for the perimeter of a rectangle, which is given by:

Perimeter = 2 * (length + width)

We also know that the area of a rectangle is given by the formula:

Area = length * width

We want to minimize the perimeter while keeping the area constant at 900. To do this, we can use the fact that for a given area, the rectangle with the smallest perimeter is a square. Therefore, to minimize the perimeter, we need to find the square with an area of 900.

Finding the Dimensions

To find the side length of the square with an area of 900, we can take the square root of the area:

Side length = √900

Taking the square root of 900 gives us the side length of the square, which is 30. Since a square is a special case of a rectangle, the dimensions of the rectangle that would result in the smallest perimeter while having an area of 900 are:

Length = 30 units Width = 30 units

So, the rectangle with dimensions of 30 units by 30 units would have the smallest perimeter for an area of 900.