Answer:
The dimensions of the screen are
Length:102 feet
Width: 82 feet
Step-by-step explanation:
we know that
The area of the rectangle (movie screen) is equal to
[tex]A=LW[/tex]
where
L is the length
W is the width
we have
[tex]A=8,364\ ft^2[/tex]
so
[tex]8,364=LW[/tex] ----> equation A
The screen is 20 feet longer than it is wide.
so
[tex]L=W+20[/tex] ---> equation B
substitute equation B in equation A
[tex]8,364=(W+20)W[/tex]
solve for W
[tex]8,364=W^2+20W\\W^2+20W-8,364=0[/tex]
solve the quadratic equation by graphing
the solution is W=82 ft
see the attached figure
Find the value of L
[tex]L=82+20=102\ ft[/tex]
therefore
The dimensions of the screen are
Length:102 feet
Width: 82 feet
