the length of a rectangular garden is 5 feet longer than its width. The garden is surrounded by a 2-foot-wide-sidewalk. The sidewalk has an area of 76 square feet. Find the dimensions of the garden

(X+4)(x+9)-x(x+5)=76

(x^2+9x+4x+36)-x(x+5)=76
x^2+13x+36-x^2-5x=76
X^2 will drop and we will combine the like terms(13x and -5x) and 36 will go to the other side
8x=76-36
8x=40
x=5

W=5ft
L=10ft since L=x+5

Let the width of the garden be x ft

then the length is x+5 ft.

area = x(x+5)

width of garden with sidewalk = x+4
length of garden with sidewalk = x+9

(x+4)(x+9) - x(x+5) = 76
solve, the x^2 will drop out

Area of living room with length being X+5 and width being 20

To find the dimensions of the garden, we can follow these steps:

Step 1: Assign variables.
Let's say the width of the garden is represented by 'w' feet.

Step 2: Express other measurements in terms of the width.
Since the length of the garden is 5 feet longer than its width, the length can be expressed as 'w + 5' feet.

Step 3: Calculate the area of the garden.
The area of the garden is calculated by multiplying the length and width. So, the area of the garden is:
Area = length x width = (w + 5) x w = w^2 + 5w.

Step 4: Account for the sidewalk.
The garden is surrounded by a 2-foot-wide sidewalk, which means each dimension of the garden should be reduced by 4 feet (2 feet on each side).
Therefore, the width with the sidewalk is w - 4, and the length with the sidewalk is (w + 5) - 4 = w + 1.

Step 5: Calculate the area of the garden with the sidewalk.
The area of the garden with the sidewalk is equal to the area of the garden plus the area of the sidewalk. Given that the area of the sidewalk is 76 square feet, we can set up the equation:
Area of garden with sidewalk = Area of garden + Area of sidewalk.

Substituting the expressions derived earlier:
(w - 4)(w + 1) = w^2 + 5w + 76.

Step 6: Solve the equation.
Expand the equation:
w^2 + w - 4w - 4 = w^2 + 5w + 76.

Combine like terms:
w - 4 = 5w + 80.

Subtract w from both sides:
-4 = 4w + 80.

Subtract 80 from both sides:
-84 = 4w.

Divide both sides by 4:
w = -21.

Ignore the negative value since the width cannot be negative.

Step 7: Calculate the dimensions of the garden.
Using the positive value for the width:
Width = w = -21 feet (ignored).
Length = Width + 5 = -21 + 5 = -16 feet (ignored).

Since we cannot have negative dimensions, we conclude that there seems to be an error or an inconsistency in the given information or calculation procedure. Please double-check the problem and ensure all values and calculations are correct.