The length of a certain rectangle is 4 meters more than three times its width. If the perimeter of the rectangle is 56 meters, then the width of the rectangle is
width ... x m
length ... 3x+4
solve 2(x + 3x+4) = 56
x+3x+4=56/2
4x+4=28
4x=28-4
4x=24
x=6
length=3x+4
=3x6+4
=18+4
=22
To find the width of the rectangle, we'll use algebra.
Let's denote the width of the rectangle as "w" (in meters).
According to the problem, the length of the rectangle is 4 meters more than three times its width. So, the length can be expressed as 3w + 4.
The formula to calculate the perimeter of a rectangle is given by:
Perimeter = 2(length + width)
Substituting the given values, we have:
56 = 2((3w + 4) + w)
Now we can solve the equation for "w".
First, distribute the 2 on the right side of the equation:
56 = 2(3w + 4) + 2w
Next, simplify:
56 = 6w + 8 + 2w
Combine like terms:
56 = 8w + 8
Subtract 8 from both sides:
56 - 8 = 8w + 8 - 8
48 = 8w
Divide both sides by 8:
48/8 = 8w/8
6 = w
Therefore, the width of the rectangle is 6 meters.
x+3x+4=56/2
4x+4=28
4x=28-4
4x=24
x=6