A square and a rectangle, the side of the square is 36cm, the perimeter of the square is equal to the perimeter

A square and a rectangle, the side of the square is 36cm, the perimeter of the square is equal to the perimeter of the rectangle, the height of the rectangle is less than the side of the square 5 times. Find the perimeter of the square and the perimeter of the rectangle. Compare the perimeter of the square and the perimeter of the rectangle.

Let’s first find the width of the rectangular shape.

To do this, divide the size of the side of the 36 cm square shape by 5.

36: 5 = 7.2 cm.

Find the perimeter of a square shape.

To do this, multiply the size of the side of the 36 cm square shape by 4.

36 x 4 = 144 cm.

This means that the perimeter of the rectangular figure is 144 cm.

Now we will find the other side of the rectangular shape.

To do this, from the perimeter of a rectangular figure of 144 cm, subtract the doubled value of the found side of a rectangular figure of 7.2 cm and divide the resulting value by 2.

144 – 7.2 x 2 = 144 – 14.4 = 129.6.

129.6: 2 = 64.8 cm.

Now let’s find the area of ​​a square shape.

To do this, multiply the value of one side of a 36 cm square shape by the value of its second side 36 cm.

36 x 36 = 1 296 cm².

Now we will find the area of ​​the rectangular shape.

To do this, we multiply each other by the obtained values ​​of its sides.

7.2 x 64.8 = 466.56 cm².

Let’s compare the areas of these two figures.

To do this, subtract the smaller one from the larger value of the area.

1,296 – 466.56 = 829.44 cm².

Answer: The perimeters of both figures are equal.

The area of ​​a square-shaped figure is 829.44 cm² larger than the area of ​​a rectangular figure.