Entries in the table what the lengths of two different sides of a rectangle can be if its perimeter is 20 cm.

Entries in the table what the lengths of two different sides of a rectangle can be if its perimeter is 20 cm. Which of these rectangles has the largest area?

Knowing that the perimeter of a rectangle is determined as the doubled sum of its sides P = 2 * (a + b), we get the value of the sum of its two sides a + b = P / 2 = 20/2 = 10 cm.

Now let’s write down what values a and b can take if their sum is 10 cm. And at the same time we will calculate the area of each of the rectangles S = a * b.

a = 1 cm, b = 9 cm. S = 9 cm2.

a = 2 cm, b = 8 cm. S = 18 cm2.

a = 3 cm, b = 7 cm. S = 21 cm2.

a = 4 cm, b = 6 cm. S = 24 cm2.

a = 6 cm, b = 4 cm. S = 24 cm2.

a = 7 cm, b = 3 cm. S = 21 cm2.

a = 8 cm, b = 2 cm. S = 18 cm2.

a = 9 cm, b = 1 cm. S = 9 cm2.

The largest area has a rectangle with side lengths 4 and 6 (or 6 and 4).