Question

Площа прямокутника 640м2 а довжина сторони 40м.Знайти площу квадрата, периметр якого дорівнює периметру прямокутника.

Answer 1

1.)640:4=160(м2.)

2.)160:4=4(м2.)

3.)4*4=16(м2.)

Ответ:16 м2

Answer 2

Calculation of the Square's Area and Perimeter

To find the area of a square with a perimeter equal to the perimeter of the given rectangle, we need to determine the length of the square's side.

Let's start by finding the perimeter of the rectangle. The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the rectangle has a length of 40m and a width that we need to determine.

The formula for the perimeter of a rectangle is:

Perimeter = 2 * (Length + Width)

Given that the perimeter of the rectangle is equal to the perimeter of the square, we can set up the following equation:

2 * (40 + Width) = 4 * Width

Simplifying the equation, we get:

80 + 2 * Width = 4 * Width

Subtracting 2 * Width from both sides, we have:

80 = 2 * Width

Dividing both sides by 2, we find:

Width = 40

Now that we have the width of the rectangle, we can calculate its area. The formula for the area of a rectangle is:

Area = Length * Width

Substituting the given values, we get:

Area = 40m * 40m = 1600m^2

Therefore, the area of the rectangle is 1600m^2.

To find the area of the square, we need to determine the length of its side. Since the perimeter of the square is equal to the perimeter of the rectangle, and we know the perimeter of the rectangle is 2 * (40 + Width), we can set up the following equation:

4 * Side = 2 * (40 + Width)

Substituting the value of Width we found earlier, we have:

4 * Side = 2 * (40 + 40)

Simplifying the equation, we get:

4 * Side = 2 * 80

Dividing both sides by 4, we find:

Side = 40

Therefore, the length of the side of the square is 40m.

Now, we can calculate the area of the square using the formula:

Area = Side * Side

Substituting the value of Side, we have:

Area = 40m * 40m = 1600m^2

Therefore, the area of the square is 1600m^2, which is the same as the area of the given rectangle.

Answer:

The area of the square, with a perimeter equal to the perimeter of the given rectangle, is 1600m^2.