Answer:
The dimensions are [tex]16[/tex] ft by [tex]32[/tex] ft
The quadratic equation is [tex]W^{2}-256=0[/tex]
Step-by-step explanation:
we know that
the area of rectangle is equal to
[tex]A=W*L[/tex]
where
L is the length side of rectangle
W is the width side of rectangle
in this problem
we have
[tex]A=512\ ft^{2}[/tex]
so
[tex]512=L*W[/tex] -----> equation A
[tex]L=2W[/tex] ------> equation B
substitute equation B in equation A
[tex]512=(2W)*W \\ 512=2W^{2} \\2W^{2}-512=0\\W^{2}-256=0[/tex]
[tex]W=\sqrt{256}=16\ ft[/tex]
Find the value of L
[tex]L=2W-----> L=2*16=32\ ft[/tex]
