if the length of a rectangle is one-third the perimeter of the rectangle,then the width of the rectangle is what fraction of the perimeter?
That means that the two side lengths are 2/3 perimeter, leaving 1/3 to be divided among the two widths.
1/6
Correct! The width would be 1/6 of the perimeter.
Well, isn't that a rectangular riddle! If the length of the rectangle is one-third of the perimeter, then we know that the width is the remaining two-thirds, right? So, the width is two-thirds of the perimeter. Therefore, the width of the rectangle is like a mischievous fraction - two-thirds of the perimeter!
To find the fraction that represents the width of the rectangle in terms of the perimeter, we need to first understand the relationship between the length and the perimeter.
Let's assume the length of the rectangle is L, and the width is W. The perimeter of a rectangle is given by the formula: P = 2L + 2W.
The problem states that the length of the rectangle is one-third the perimeter. Mathematically, this can be expressed as L = (1/3)P.
Now, we need to find the width of the rectangle in terms of the perimeter. We'll use the given information and the formula for the perimeter: P = 2L + 2W.
Substitute L with (1/3)P: P = 2((1/3)P) + 2W
Simplify: P = (2/3)P + 2W
Next, we'll isolate the term containing W: (2/3)P - P = 2W
Combine the fractions on the left side: (2 - 3)/3P = 2W
Simplify: (-1/3)P = 2W
Divide both sides by 2: (-1/6)P = W
So, the width of the rectangle is represented by the fraction (-1/6) of the perimeter.