Answer:
[tex]Width = 2\frac{1}{4}cm[/tex]
[tex]Length=5\frac{5}{12} cm[/tex]
Step-by-step explanation:
Data from the question;
Perimeter of a rectangle is [tex]15\frac{1}{3}[/tex] cm
Length is [tex]3\frac{1}{6}[/tex] cm longer than the width
We are supposed to determine the length and the with of the rectangle;
Assuming, the width x cm
Then, the length is [tex]x+3\frac{1}{6}[/tex] cm
We need to know that the perimeter of a rectangle is given by;
Perimeter = 2 ( length + width)
Therefore;
[tex]15\frac{1}{3}= 2 ( x + (x+3\frac{1}{6}))[/tex]
[tex]15\frac{1}{3}=2(2x+3\frac{1}{6})[/tex]
Thus;
[tex]15\frac{1}{3}=4x+6\frac{1}{3}[/tex]
[tex]4x=9\\x=2\frac{1}{4}[/tex]
Therefore;
[tex]Width = 2\frac{1}{4}cm[/tex]
[tex]Length = x + 3\frac{1}{6}[/tex]
[tex]=2\frac{1}{4}+3\frac{1}{6}[/tex]
[tex]=5\frac{5}{12} cm[/tex]
Therefore; the length is [tex]5\frac{5}{12}[/tex] cm while the width is [tex]2\frac{1}{4}[/tex] cm
