Respuesta :
Answer:
Step-by-step explanation:
let x and y be length and width of rectangle.
Perimeter=2(x+y)
area=xy
2(x+y)=1/2 xy
4(x+y)=xy
4x+4y=xy
x y-4y=4 x
y(x-4)=4 x
[tex]y=\frac{4x}{x-4}[/tex]
The length of the rectangle in terms of the width is [tex]\rm W = \dfrac{4L}{L-4}[/tex].
Given that,
The perimeter of a rectangle equals one and a half times its area.
We have to determine,
The length of the rectangle in terms of the width.
According to the question,
Let the width of the rectangle be W,
And the length of the rectangle is L.
The perimeter of the rectangle is,
[tex]\rm \ Perimeter \ of \ rectangle = 2(L+ W)[/tex]
And the area of the rectangle is,
[tex]\rm \ Area \ of \ the \ rectangle = L \times W[/tex]
Where L is the length of the rectangle and W is the width of the rectangle.
The perimeter of the rectangle equals one and a half times its area.
Then,
[tex]\rm Perimeter \ of \ rectangle = \dfrac{1}{2} \ Area \ of \ rectangle\\\\2 (L+w) = \dfrac{1}{2} \times L \times W[/tex]
Therefore,
The length of the rectangle in terms of the width is,
[tex]\rm 2 (L+w) = \dfrac{1}{2} \times L \times W \\\\2\times2 (L+w) =L \times W\\\\4 (L+w) =L \times W\\\\\\4L+4W = LW\\\\4L = LW-4W\\\\4L = W(L-4)\\\\W = \dfrac{4L}{L-4}[/tex]
Hence, The length of the rectangle in terms of the width is [tex]\rm W = \dfrac{4L}{L-4}[/tex].
For more details refer to the link given below.
https://brainly.com/question/8177812
