The length of a rectangular garden is 4 m greater than the width. the area is 77m^2. find the dimensions of the garden.

W(w+4)=77

W^2 + 4w - 77 = 0
(W-7)(w+11)=0
W-7=0
W=7

W+11=0 gives neg. ans.

Length = 7+4=11
Width = 4

12

To find the dimensions of the garden, we need to set up an equation based on the given information.

Let's represent the width of the garden as "x" meters.

According to the problem, the length of the garden is 4 meters greater than the width. So, the length of the garden would be "x + 4" meters.

The area of a rectangle is calculated by multiplying its length and width. In this case, we have:

Area = Length * Width

Given that the area is 77 square meters, we can write this equation as:

77 = (x + 4) * x

Now, let's solve this equation step by step to find the dimensions of the garden.

Step 1: Distribute the multiplication
77 = x^2 + 4x

Step 2: Rearrange the equation into a quadratic form
x^2 + 4x - 77 = 0

Step 3: Factorize the equation or use the quadratic formula to solve for x. Let's use factoring in this case.
(x - 7)(x + 11) = 0

Setting each factor to zero, we get:

x - 7 = 0 or x + 11 = 0

Solving these equations separately, we find two possible solutions for x:

x = 7 or x = -11

Since the dimensions of a garden cannot be negative, we discard the solution x = -11.

Therefore, the width of the garden is x = 7 meters.

To find the length, we can substitute this value back into the equation:

Length = Width + 4

Length = 7 + 4

Length = 11 meters

So, the dimensions of the garden are 7 meters for width and 11 meters for length.

To find the dimensions of the rectangular garden, we can use the given information and set up equations based on the problem statement.

Let's assume that the width of the garden is "x" meters. Then, according to the problem, the length of the garden is 4 meters greater than the width, so it would be "x + 4" meters.

The area of a rectangle can be calculated by multiplying its length by its width. Therefore, we can form the equation:

Area = Length * Width

From the problem, we know that the area is 77 square meters, so we can substitute the values into the equation:

77 = (x + 4) * x

Now, let's solve this quadratic equation to find the dimensions of the garden.

Expanding the equation:

77 = x^2 + 4x

Rearranging the equation:

0 = x^2 + 4x - 77

To solve this quadratic equation, we can factor it, use the quadratic formula, or complete the square. In this case, let's use factoring:

0 = (x + 11)(x - 7)

Setting each factor equal to zero:

x + 11 = 0 or x - 7 = 0

Solving for x in each equation:

x = -11 or x = 7

Since we are dealing with dimensions, a negative value for x does not make sense, so we reject the solution x = -11.

Therefore, the width of the rectangular garden is x = 7 meters.

To find the length, we can substitute the width value back into the equation:

Length = Width + 4
Length = 7 + 4
Length = 11 meters

So, the dimensions of the garden are width = 7 meters and length = 11 meters.