The perimeter of a recatangle is twice the sum of its length and its width. The perimeter is 16 meters and its length is 2 meters more than twice its width.What is the length?
w = width
(2+2w) = length
perimeter = 2[w+(2+2w)] =16
w+2+2w = 8
3 w = 6 etc
16 = 2L + 2W)
L = 2W + 2.
Solve the two equations for L and W.
By substitution, you can see that
16 = 2L + L - 2 = L - 2
The ratio of men to women in a certain factory is 3:4. There are 210 men. How many workers are there?
Answer is 280
x = (4/3) * 210 = 280
M/W = 3/4
M = 210
W = 280
M + W = ?
The number of women is 280, but the total number of workers is something else.
To find the length of the rectangle, we need to set up an equation using the given information.
Let's start by labeling the length as L and the width as W.
The problem states that "the perimeter of a rectangle is twice the sum of its length and its width." We can translate this into an equation:
Perimeter = 2 × (Length + Width)
Since the perimeter is given as 16 meters, we can substitute this value into the equation:
16 = 2 × (L + W)
Next, the problem states that "the length is 2 meters more than twice its width." We can translate this into another equation:
Length = 2 × Width + 2
Now we have two equations that represent the given information. We can solve these equations simultaneously to find the values of Length and Width.
Let's substitute the value of Length from the second equation into the first equation:
16 = 2 × ((2 × Width) + 2) + Width
Next, simplify the equation:
16 = 4 × Width + 4 + Width
Combine like terms:
16 = 5 × Width + 4
Now, isolate the term with Width:
16 - 4 = 5 × Width
12 = 5 × Width
Finally, solve for Width:
Width = 12 / 5
Width = 2.4
Now that we know the Width is 2.4 meters, we can substitute it back into the second equation to find the Length:
Length = 2 × Width + 2
Length = 2 × 2.4 + 2
Length = 4.8 + 2
Length = 6.8
Therefore, the length of the rectangle is 6.8 meters.