Question

Периметер прямоугольника 36 дм основании на 6 см больше высоты найдите стороны прямоугольника

Answer 1

Периметр прямоугольника мы находим по формуле Р=(а+б)*2
Пусть х-высота  прямоугольника,тогда х+6-основание 
36=(х+(х+6))*2
2х+6=18
2х=12
х=6-высота,6+6=12-основание 

Answer 2

Perimeter of a Rectangle

To find the sides of a rectangle when the perimeter is given, we can use the formula for the perimeter of a rectangle, which is:

Perimeter (P) = 2 * (Length (L) + Width (W)) In this case, the perimeter of the rectangle is given as 36 dm, and the base is 6 cm longer than the height. Let's assume the height of the rectangle is 'h' cm.

According to the given information, the base (length) of the rectangle is 6 cm longer than the height. So, the length (L) of the rectangle can be expressed as:

Length (L) = Height (h) + 6 cm

Substituting this value into the perimeter formula, we get:

36 dm = 2 * (h + 6 cm + h)

Now, let's solve this equation to find the value of 'h' and then calculate the sides of the rectangle.

Solving the Equation

To solve the equation, we need to convert the units to be consistent. Since the perimeter is given in decimeters (dm) and the height is given in centimeters (cm), we need to convert the height to decimeters.

1 cm = 0.1 dm

So, the height in decimeters (h_dm) can be calculated as:

Height (h_dm) = Height (h) * 0.1 dm/cm

Substituting this value into the equation, we get:

36 dm = 2 * (h_dm + 6 cm + h_dm)

Simplifying the equation, we have:

36 dm = 2 * (2h_dm + 6 cm)

Dividing both sides of the equation by 2, we get:

18 dm = 2h_dm + 6 cm

Now, let's convert the height from centimeters to decimeters:

Height (h_dm) = Height (h) * 0.1 dm/cm = h * 0.1 dm/cm

Substituting this value into the equation, we get:

18 dm = 2 * (2h * 0.1 dm/cm + 6 cm)

Simplifying the equation further, we have:

18 dm = 2 * (0.2h_dm + 6 cm)

Now, let's convert the centimeters to decimeters:

6 cm = 6 cm * 0.1 dm/cm = 0.6 dm

Substituting this value into the equation, we get:

18 dm = 2 * (0.2h_dm + 0.6 dm)

Simplifying the equation again, we have:

18 dm = 0.4h_dm + 1.2 dm

Subtracting 1.2 dm from both sides of the equation, we get:

16.8 dm = 0.4h_dm

Dividing both sides of the equation by 0.4, we get:

h_dm = 42 dm

Now that we have the value of the height in decimeters, we can calculate the length (L) and width (W) of the rectangle.

The length (L) can be calculated as:

Length (L) = Height (h_dm) + 6 cm

Substituting the values, we get:

Length (L) = 42 dm + 6 cm * 0.1 dm/cm = 42 dm + 0.6 dm = 42.6 dm

The width (W) can be calculated as:

Width (W) = Height (h_dm)

Substituting the value, we get:

Width (W) = 42 dm

Therefore, the sides of the rectangle are:

Length (L) = 42.6 dm Width (W) = 42 dm

Please note that the values have been rounded to one decimal place for simplicity.

I hope this helps! Let me know if you have any further questions.