the perimeter of a rectangular garden is 132 meters.The length is 6meters longer than twice the width. Find the demensions of the garden.
L + W = 66
L - 2W = 6
Solve simultaneously
3 W = 60
W = ___
L = 66 - W = ___
Let's start by assigning variables to the dimensions of the garden. Let's call the width "w" and the length "l".
Based on the given information, we can create the following equations:
1) The perimeter of a rectangle is given by the formula P = 2l + 2w.
2) The length is 6 meters longer than twice the width, so we can write the equation l = 2w + 6.
We know that the perimeter of the garden is 132 meters, so we can set up the equation:
132 = 2l + 2w
Now, let's substitute the value of l from equation 2 into equation 1:
132 = 2(2w + 6) + 2w
Simplify the equation:
132 = 4w + 12 + 2w
Combine like terms:
132 = 6w + 12
Subtract 12 from both sides:
120 = 6w
Divide both sides by 6:
w = 20
Now, we can substitute the value of w back into equation 2 to find the length:
l = 2w + 6
l = 2(20) + 6
l = 40 + 6
l = 46
Therefore, the dimensions of the garden are width = 20 meters and length = 46 meters.
To find the dimensions of the garden, we need to set up equations based on the given information.
Let's assume that the width of the garden is "w" meters. According to the problem, the length is 6 meters longer than twice the width, so the length would be 2w + 6 meters.
The perimeter of a rectangle can be calculated by adding the lengths of all the sides. In this case, the perimeter is given as 132 meters. We can set up the equation:
Perimeter = 2 * (Length + Width)
From the problem, we have:
132 = 2 * (2w + 6 + w)
Now, we need to solve this equation for "w" in order to find the width of the garden.
Let's simplify the equation:
132 = 2 * (3w + 6)
132 = 6w + 12
Subtract 12 from both sides:
120 = 6w
Divide both sides by 6:
w = 20
Now that we have the width, we can substitute this value back into one of our earlier equations to find the length.
Length = 2w + 6
Length = 2(20) + 6
Length = 40 + 6
Length = 46
So, the dimensions of the garden are width = 20 meters and length = 46 meters.