The perimeter of a rectangular garden is 108 meters. The length is 6 meters longer than twice the width. Find the dimensions of the garden.

P = 2L + 2W

108 = 2(2W + 6) + 2W

108 = 6W + 12

96 = 6W

16 = W

width = 16m

length = 38m

Why did the scarecrow win an award? Because he was outstanding in his field! Now, let's solve this garden mystery together.

Let's say the width of the garden is x meters. According to the problem, the length is 6 meters longer than twice the width, which means the length = 2x + 6.

The formula for the perimeter of a rectangle is P = 2(length + width), so we can write the equation as:
108 = 2(2x + 6 + x)

Simplifying this equation, we get:
108 = 2(3x + 6)
54 = 3x + 6
48 = 3x
x = 16

So, the width of the garden is 16 meters. To find the length, we can substitute the value of x in the expression 2x + 6:
Length = 2(16) + 6
Length = 38

Therefore, the dimensions of the garden are 16 meters by 38 meters.

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

Let's assume the width of the garden is "w" meters.
According to the problem, the length is 6 meters longer than twice the width, which can be expressed as "2w + 6" meters.

The perimeter of a rectangle is calculated by adding the lengths of all its sides. For a rectangular garden, we have two equal lengths and two equal widths. Therefore, we can write the equation:

Perimeter = 2*(length + width)

In our case, the perimeter is given as 108 meters. Plugging in the values, we get:

108 = 2*((2w + 6) + w)

Now, we can simplify and solve the equation to find the value of "w".

108 = 2*(3w + 6)

Divide both sides of the equation by 2:
54 = 3w + 6

Subtract 6 from both sides:
48 = 3w

Divide both sides by 3:
16 = w

So, the width of the garden is 16 meters.

Now, we can find the length by substituting the value of the width back into the expression for the length:

Length = 2w + 6
Length = 2(16) + 6
Length = 32 + 6
Length = 38

Therefore, the dimensions of the garden are:

Width = 16 meters
Length = 38 meters

Didn’t work

did never work 💮