The area of the square is 64 cm2. Find the area of a rectangle whose perimeter is equal to the perimeter

The area of the square is 64 cm2. Find the area of a rectangle whose perimeter is equal to the perimeter of the given square, if one of its sides is 3 times larger than the other.

1. The first step is to calculate the length of the side of the square using the formula, the square root of the area value:

√64 = 8 cm.

2. The second step is to calculate the perimeter of the square:

8 * 4 = 32 cm.

3. The perimeter of the rectangle is, according to the condition, 32 cm. Let one side be equal to x cm, then the other side is equal to 3x cm.

The perimeter of a rectangle is calculated by the formula the sum of its length and width, multiplied by two:

2 * (x + 3x) = 32.

2 * 4x = 32.

8x = 32.

x = 32: 8.

x = 4.

4. For x we ​​took the value of the width of the rectangle, we calculate the value of the length of the rectangle:

4 * 3 = 12 cm.

5. Calculate the area of ​​a rectangle using the formula the product of its length and width:

4 * 12 = 48 cm2

Answer: the area of ​​the rectangle is 48 cm2