Answer :
Answer:
Width = 6 units
Length = 12 units
Step-by-step explanation:
First thing first :)
The area of a rectangle is given by the formula:
[tex]A=wl[/tex]
where
[tex]A[/tex] is the area of the rectangle
[tex]w[/tex] is the width
[tex]l[/tex] is the length
On the other hand, the perimeter of a rectangle is given by:
[tex]P=2(w+l)[/tex]
where
[tex]P[/tex] is the perimeter
[tex]w[/tex] is the width
[tex]l[/tex] is the length
We know from our problem that the area of our rectangle is twice its perimeter, so:
[tex]A=2(2)P[/tex]
[tex]A=4P[/tex]
[tex]wl=4(w+l)[/tex]
We also know that its length is twice its width, so [tex]l=2w[/tex]. Let's replace that value in our previous equation and simplify:
[tex]w(2w)=4(w+2w)[/tex]
[tex]2w^2=4(3w)[/tex]
[tex]2w^2=12w[/tex]
Subtract [tex]12w[/tex] from both sides of the equation:
[tex]2w^2-12w=12w-12w[/tex]
[tex]2w^2-12w=0[/tex]
Factor [tex]w[/tex]:
[tex]w(2w-12)=0[/tex]
Equate both factor to zero:
[tex]w=0, 2w-12=0[/tex]
A length can't be zero, so discard [tex]w=0[/tex] and solve for the other one:
[tex]2w-12=0[/tex]
[tex]2w=12[/tex]
[tex]w=\frac{12}{2}[/tex]
[tex]w=6[/tex]
Know that we have the width of our rectangle, we can find its length:
[tex]l=2w[/tex]
[tex]l=2(6)[/tex]
[tex]l=12[/tex]
We can conclude that the width of our rectangle is 6 units and its length is 12 units.