The sides of the rectangle are 5 1/3 cm and 8 5/6 cm. Find the perimeter of a square

The sides of the rectangle are 5 1/3 cm and 8 5/6 cm. Find the perimeter of a square with an area of 18/9 cm2 larger than the area of this rectangle.

Find the area S of a rectangle with sides 5 1/3 cm and 8 5/6 cm.

To do this, convert the expressions 5 1/3 and 8 5/6 to improper fractions:

5 1/3 = 5 + 1/3 = 15/3 + 1/3 = 16/3;

8 5/6 = 8 + 5/6 = 48/6 + 5/6 = 53/6.

Now we can calculate the area of ​​this rectangle:

S = 16/3 * 53/6 = 8/3 * 53/3 = 424/9 cm².

Find the area of ​​the square.

According to the problem statement, the area of ​​the square is 1 8/9 cm² larger than the area of ​​this rectangle.

Since 1 8/9 = 1 + 8/9 = 9/9 + 8/9 = 17/9, the area of ​​the square is:

424/9 + 17/9 = 441/9 = 49 cm².

Find the side length of the square.

Let us denote it by x.

The area of ​​any square is equal to the length of the side of this square in the second degree, therefore, we can make the following equation:

x² = 49.

We solve the resulting equation:

x² = (7) ²;

x = 7 cm.

Find the perimeter P of the square:

P = 4 * 7 = 28 cm.

Answer: the perimeter of the square is 28 cm.