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