Answer
The dimensions of the rectangle is $6 units$ by $12 units$
Work Step by Step
Given:
$A=2P$
$L×W = 2(2L+2W)$
$L=2W$
Substitute L to the working equation and simplify
$L×W = 2(2L+2W)$
$2W×W = 2(2(2W)+2W)$
$2W^2 = 2(4W + 2W)$
$2W^2 = 2(6W)$
Divide each side by 2
$W^2 = 6W$
Use factoring and zero product property to identy the solution
$W^2 - 6W = 0$
$W(W - 6) = 0$
The equation has 2 solutions
$W = 0$
$W = 6$
We must disregard $W=0$ because the width will not have a 0 value so the width of the rectangle is 6 units.
$W=6 units$
To find the length:
$L=2W$
$L=2×6$
$L=12 units$
