The perimeter is an enclosed area of any two or one-dimensional shape.
The perimeter of a rectangle is given by:
[tex]\rm P = 2 ( L + B )[/tex]
The length is [tex]\rm 2 \dfrac{2}{5} feet[/tex] and the width of the rectangle is [tex]\rm 1\dfrac{4}{5} feet[/tex].
This can be calculated by:
Given,
- Perimeter (P) = [tex]\rm 8 \dfrac{2}{5} feet[/tex]
Let,
Since,
3L = 4W
[tex]\rm L = \dfrac{4W}{3}[/tex]
Substituting the value of L in the equation of perimeter:
[tex]\rm 2(\dfrac{4W}{3}) + 2W = 8 \dfrac{2}{5}[/tex]
[tex]\rm \dfrac{8W}{3} + 2W = 8 \dfrac{2}{5}[/tex]
Now multiplying the left and right sides by 3 we get:
[tex]\rm 8W+6W = 24 \dfrac{6}{5}[/tex]
[tex]\rm 14W = 25 \dfrac{1}{5}[/tex]
Now divide both sides by 14:
[tex]\rm \dfrac{14W}{14} =\dfrac{(25 \dfrac{1}{5})}{14}[/tex]
[tex]\rm W = \dfrac{(\dfrac{126}{5})}{14} \\\\= \dfrac{9}{5}[/tex]
[tex]\rm W = 1 \dfrac{4}{5}[/tex]
Now substituting the value of W, length can be calculated:
[tex]\rm L = \dfrac{4(1 \dfrac{4}{5})}{3}[/tex]
[tex]\rm L = \dfrac{(4)\dfrac{9}{5}}{3} \\\\= \dfrac{(\dfrac{36}{5})}{3} \\\\= \dfrac{12}{5}[/tex]
[tex]\rm L = 2 \dfrac{2}{5}[/tex]
Therefore, length is [tex]\rm 2 \dfrac{2}{5} feet[/tex] and width is [tex]\rm 1\dfrac{4}{5} feet[/tex].
To learn more about the perimeter of rectangle follow the link:
https://brainly.com/question/8966512
