Question

Клумба прямоугольной формы окружена дорожкой , ширина которой 1 м. S дорожки 36 м². Найдите стороны клумбы , если одна из них на 6 м больше другой СРОЧНО​

Answer 1

Объяснение:

Ширина клумбы=х м

Длина клумбы=х+6 м

Ширина дорожки=1 м

Sд=36 м^2

Sкл=х(х+6) см^2

Sпрямоуг=Sкл+Sд

Sпрям=(ширина клумбы+1+1)×(длина клумбы+1+1)=

=(х+1+1)×((х+6+1+1)=(х+2)(х+8) см^2

(х+2)(х+8)=х(х+6)+36

Х^2+8х+2х+16=х^2+6х+36

10х-6х=36-16

4х=20

Х=5 м - ширина клумбы

5+6=11 м - длина клумбы

Answer 2

Calculating the Dimensions of the Flower Bed

To find the dimensions of the rectangular flower bed, we can use the given information about the width of the surrounding path and the area of the path.

Let's denote the length of the flower bed as L and the width as W.

The total area of the flower bed and the path is the area of the flower bed plus the area of the path. We can express this as an equation:

Total area = (L + 2) * (W + 2) = L * W + 36

Given that one side of the flower bed is 6 meters longer than the other, we can express this as another equation:

L = W + 6

Now, we can solve these equations to find the dimensions of the flower bed.

Solving for the Dimensions

Substitute the expression for L from the second equation into the first equation:

(W + 6 + 2) * (W + 2) = (W + 6) * W + 36

Simplify and solve for W:

W^2 + 8W + 12 = W^2 + 6W + 36

2W = 24

W = 12

Now that we have the width, we can find the length:

L = W + 6 = 12 + 6 = 18

Conclusion

The dimensions of the rectangular flower bed are: - Length (L): 18 meters - Width (W): 12 meters