A square and a rectangle have the same perimeter – 20 cm. Find out the area of a rectangle

A square and a rectangle have the same perimeter – 20 cm. Find out the area of a rectangle if its width is 3 cm. Which shape is larger and by how much?

The area of ​​a rectangle is calculated as the product of its length and width. Since we know the perimeter and width of the rectangle, therefore, we can find its length. We also know that the sides of the rectangle are pairwise equal:

20 – 3 * 2 = 20 – 6 = 14 cm – the sum of the two lengths of the rectangle,

14: 2 = 7 cm – the length of the rectangle.

Let’s calculate the area of ​​the rectangle:

S = 3cm * 7cm = 21cm2.

For a square, all sides are equal to each other, that is, we can find the length of the side of the square:

20: 4 = 5 cm.

Find the area of ​​the square:

S = 52 = 25 cm2.

Thus, we can conclude that the area of ​​the square is greater than the area of ​​the rectangle by:

25 – 21 = 4 cm2.

Answer: the area of ​​the square is 4 cm2 larger.