Question

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? guys i need help

Answer 1

the booths are square so allow then to have a side length of x feet

the length of the 10 booths is 10x

the wide of the booth is x

4 feet is added to each end so the length of the area is 10x + 8

4 feet us added to the width so the width is x + 4

and the total area is 2300

set up the equation

Area = length x width

2300 = (10x +8)(x + 4)

then 10x^2 +48x + 32 = 2300

5x^2 + 24x - 1134 = 0


you'll need the general quadratic formula I think

\[x = \frac{-24 \pm \sqrt{24^2 - 4 \times 5\times(-1134)}}{2\times5}\]

\[x= \frac{-24\pm \sqrt{23256}}{10}\]

so the edge length is the positive measurement only

\[x = \frac{\sqrt{23256} - 24}{10}\]

each booth has a side length of 10.45 feet