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physics convention 11 companies set up equal sized square booths in a row along one wall of a convention center.The booths are adjacent to each other and a 2-ft wide walkway surrounds the block of booths on three sides. The total area of the booths and walkway is 1200 ft^2. What is the side length of each booth?

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Answer:

Side length of each booth is 8.35 ft approximately.

Step-by-step explanation:

There are 11 companies set up equal sized square booths in a row along one wall of a convention center.

Now, refer the diagram to answer the problem.

It is given area is 1200.

So, length x width =1200

(11x+24)(x+2)=1200

Multiply using FOIL method.

[tex]11x^{2}[/tex]+22x+24x+48=1200

[tex]11x^{2}[/tex]+46x+48-1200=0

[tex]11x^{2}[/tex]+46x-1152=0

Solve using quadratic formula

x=[tex]\frac{-46+/- \sqrt{46^{2}-4(11)(-1152 } }{2(11)}[/tex]

x=[tex]\frac{-46+/-\sqrt{2116+50688} }{22}[/tex]

x=[tex]\frac{-46+/-\sqrt{52804} }{22}[/tex]

Simplify it

[tex]x=\frac{-49+/- 229.79}{22}[/tex]

Simplify to get two values for x.

x=8.35; x=-12.67

Here negative does not work.

Side length of each booth is 8.35 ft.

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