Question

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?

Answer 1

Side length of each booth is 8.35 ft approximately.

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.

`11x^(2)`+22x+24x+48=1200

`11x^(2)`+46x+48-1200=0

`11x^(2)`+46x-1152=0

Solve using quadratic formula

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

x=
`(-46+/-√(2116+50688) )/(22)`

x=
`(-46+/-√(52804) )/(22)`

Simplify it

`x=(-49+/- 229.79)/(22)`

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.