The perimeter of a rectangle is 122m. The length of the rectangle is 11m less than 5 times the width. Find the dimensions of the rectangle.

P = Perimeter

L = Length

W = Width

P = 2 L + 2 W

P = 2 ( L + W )

P = 122 m

L = 5 W - 11

122 = 2 ( 5 W - 11 + W )

122 = 2 ( 6 W - 11 )

122 = 12 W - 22

122 + 22 = 12 W

12 W = 144 Diwidw both sides with 12

W = 144 / 12

W = 12 m

L = 5 W - 11

L = 5 * 12 - 11

L = 60 - 11

L = 49 m

P = 2 ( L + W )

P = 2 ( 49 + 12 )

P = 2 * 61

P = 122 m

Let's assume the width of the rectangle is "w" meters.

According to the given information, the length of the rectangle is 11 meters less than 5 times the width, which can be written as:

Length = 5w - 11

The formula for the perimeter of a rectangle is:

Perimeter = 2(Length + Width)

Substituting the values we have:

122 = 2(5w - 11 + w)

122 = 2(6w - 11)

122 = 12w - 22

12w = 122 + 22

12w = 144

w = 144 / 12

w = 12

So, the width of the rectangle is 12 meters.

Now, let's calculate the length using the equation we found earlier:

Length = 5w - 11

Length = 5(12) - 11

Length = 60 - 11

Length = 49

Therefore, the dimensions of the rectangle are: width = 12 meters and length = 49 meters.

To find the dimensions of the rectangle, we can set up two equations based on the given information.

Let's assume the width of the rectangle is represented by 'w' meters. From the given information, we know that the length of the rectangle is 11m less than 5 times the width. Therefore, the length can be represented as (5w - 11) meters.

Now, we can use the formula for the perimeter of a rectangle to set up the first equation:

Perimeter = 2(Length + Width)

Substituting the given perimeter value of 122m and the expressions for length and width, we get:

122 = 2((5w - 11) + w)

Simplifying the equation:
122 = 2(6w - 11)
61 = 6w - 11
6w = 61 + 11
6w = 72
w = 12

Now that we have calculated the width, we can substitute this value back into one of the equations to find the length:

Length = 5w - 11
Length = 5(12) - 11
Length = 60 - 11
Length = 49

Therefore, the dimensions of the rectangle are:
Width = 12m
Length = 49m