the perimeter of a rectangle is twice the sum of its length and its width. the perimeter is 40 meters and its lenth is 2 meters more then twice its width. what is the length?
P = 2(L + W) = 40m,
P = 2L + 2W = 40,
L = (2W + 2)m,
P = 2(2W + 2) + 2W = 40,
4W + 4 + 2W = 40,
6W = 36,
W = 6m.
L = 2W + 2 = 2*6 + 2 = 14m.
Let's break down the information given:
1. The perimeter of a rectangle is twice the sum of its length and its width.
2. The perimeter is 40 meters.
3. The length is 2 meters more than twice its width.
Let's solve the problem step-by-step:
Step 1: Let's assume the width of the rectangle is "W" meters.
Step 2: According to the given information, the length is 2 meters more than twice its width. So, the length can be represented as "2W + 2".
Step 3: The perimeter of a rectangle is given by the formula: 2(length + width).
From the given information, we can form the equation:
2((2W + 2) + W) = 40
Simplifying the equation:
2(3W + 2) = 40
6W + 4 = 40
6W = 36
W = 6
Step 4: Now that we have the value of the width (W = 6), we can find the length.
Length = 2W + 2 = 2(6) + 2 = 12 + 2 = 14 meters.
Therefore, the length of the rectangle is 14 meters.
To find the length of the rectangle, we can set up a system of equations based on the given information.
Let's assume:
Width of the rectangle = x meters
Length of the rectangle = 2x + 2 meters (2 meters more than twice the width)
According to the problem, the perimeter of the rectangle is twice the sum of its length and width. The formula for perimeter is:
Perimeter = 2 × (Length + Width)
Plugging in the values, we get:
40 = 2 × (2x + 2 + x)
Simplifying the equation:
40 = 2 × (3x + 2)
Now, we can solve the equation to find the value of x.
Dividing both sides by 2:
20 = 3x + 2
Subtracting 2 from both sides:
18 = 3x
Dividing both sides by 3:
x = 6
So, the width of the rectangle is 6 meters.
To find the length, substitute this value back into the equation for length:
Length = 2x + 2
Length = 2(6) + 2
Length = 12 + 2
Length = 14
Therefore, the length of the rectangle is 14 meters.