the length of a certain rectangle is 3 meters more than twice its width.what is the width of rectangle if the perimeter of the rectangle is 150 meters?
L = 2W+3
2L + 2W = 150
Substitute 2W+3 for L in the second equation and solve for W.
24
Oh, I see we have a rectangular mystery on our hands. Let's call the width of the rectangle "W". According to the information provided, the length is 3 meters more than twice the width, which means it can be expressed as (2W + 3).
Now, let's work on finding the perimeter using the formula P = 2L + 2W. Since the perimeter is given as 150 meters, we can substitute the known values into the equation:
150 = 2(2W + 3) + 2W
Simplifying, we have:
150 = 4W + 6 + 2W
Combining like terms gives us:
150 = 6W + 6
Subtracting 6 from both sides, we get:
144 = 6W
Dividing both sides by 6, we find:
W = 24
So, the width of the rectangle is 24 meters.
Let's start by assuming the width of the rectangle as "x" meters.
According to the given information, the length of the rectangle is 3 meters more than twice its width.
Therefore, the length would be (2x + 3) meters.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
From the problem, the perimeter is given as 150 meters.
So, we can set up the equation as follows:
150 = 2((2x + 3) + x)
Let's solve this equation step-by-step:
150 = 2(3x + 3) [Distribute the 2]
150 = 6x + 6 [Combine like terms]
Subtracting 6 from both sides:
150 - 6 = 6x
144 = 6x
Dividing both sides by 6:
144/6 = x
24 = x
Therefore, the width of the rectangle is 24 meters.
To find the width of the rectangle, let's assign a variable to represent it. Let's call the width "w".
According to the problem, the length of the rectangle is 3 meters more than twice its width. Hence, the length can be expressed as 2w + 3.
The perimeter of a rectangle is calculated by adding the lengths of all its sides, which in this case is twice the sum of the length and width.
Based on the information given, we can write an equation to find the width:
Perimeter = 2(length + width)
150 = 2(2w + 3 + w)
Now, let's solve this equation to find the value of "w":
150 = 2(3w + 3)
150 = 6w + 6
144 = 6w
w = 24
Therefore, the width of the rectangle is 24 meters.