At a physics convention, 10 companies set up equal sized square booths in a row along one wall of the convention center. The booths are adjacent to each other and a 4-ft wide walkway surrounds the block of booths on three sides. The total area of the booths and walkway is 2300 ft^2. What is the side length of each booth?

Question

anonymous · Answer

|dw:1353083813906:dw| length of the booths plus the walkway is 8+l and width is 4+w. Also since the booths are square we can determine that l=10w. we know area =lw=2300 so (8+l)(4+w)=2300 sub in l=10w for l go get
(8+10w)(4+w)=2300 develop this to get
32+40w+8w+10w^2=2300 and solve for w
-2268+48w+10w^2=0 use quadratic formula to get w=12.84 so each booth is 12.84 ft by 12.84 ft