The length of a rectangle is 2 more than 3 times the width. If the perimeter is 100 meters, what is the width of the rectangle?
2(x+y) = 100
But, y = 3x+2, so
2(x+3x+2) = 100
...
P = 2L + 2W
100 = 2(3W + 2) + 2W
100 = 8W + 4
96 = 8W
12 = W
Let's assume the width of the rectangle is "W" meters.
According to the given information, the length of the rectangle is 2 more than 3 times the width, so the length can be expressed as (3W + 2) meters.
The perimeter of a rectangle is the sum of all its sides, so we can calculate it using the formula: Perimeter = 2 × (length + width).
In this case, the perimeter of the rectangle is 100 meters, so we can set up the equation: 100 = 2 × (3W + 2 + W).
Let's solve the equation step-by-step to find the value of W:
1. Distribute the 2 on the right side of the equation: 100 = 2(4W + 2).
Simplifying: 100 = 8W + 4.
2. Subtract 4 from both sides of the equation: 100 - 4 = 8W.
Simplifying: 96 = 8W.
3. Divide both sides of the equation by 8: 96/8 = W.
Simplifying: 12 = W.
Therefore, the width of the rectangle is 12 meters.
To find the width of the rectangle, let's make use of the given information and set up an equation.
Let's say the width of the rectangle is "w" meters. According to the problem, the length of the rectangle is 2 more than 3 times the width, which can be written as 3w + 2.
The formula for the perimeter of a rectangle is P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
In this case, we have 2 equations:
P = 100 (since the perimeter is given as 100 meters)
P = 2(l + w) (perimeter formula)
Now we can substitute the values into the second equation:
100 = 2((3w + 2) + w)
Simplifying the equation:
100 = 2(4w + 2)
100 = 8w + 4
96 = 8w
w = 12
Therefore, the width of the rectangle is 12 meters.