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 ft2. What is the side length of each booth?
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To solve this problem, you have to set up an equation for the area where your variable will be the length of each side of the square booths.
We will say that the length of each side is equal to x.
Now start finding the individual areas of the walkway and booth area and set up an equation.
Area=8x+32+40x+x*(10x)
=48x+10x^2+32
=10x^2+48x+32
From the problem statement, we know that the area is 2300ft^2. We can now plug that value into the equation that we made and solve for x (the side length of each booth).
2300=10x^2+48x+32
To find x, we can use the quadratic equation:
x=[-b+/-sqrt(b^2-4ac)]/(2a)
a=10
b=48
c=32
Therefore:
x=[-48+/-sqrt(48^2-4*10*32)]/(2*10)
x=12.85ft or x=-17.65ft
Since the booths can't have a negative side length, the answer is x=12.85ft
We will say that the length of each side is equal to x.
Now start finding the individual areas of the walkway and booth area and set up an equation.
Area=8x+32+40x+x*(10x)
=48x+10x^2+32
=10x^2+48x+32
From the problem statement, we know that the area is 2300ft^2. We can now plug that value into the equation that we made and solve for x (the side length of each booth).
2300=10x^2+48x+32
To find x, we can use the quadratic equation:
x=[-b+/-sqrt(b^2-4ac)]/(2a)
a=10
b=48
c=32
Therefore:
x=[-48+/-sqrt(48^2-4*10*32)]/(2*10)
x=12.85ft or x=-17.65ft
Since the booths can't have a negative side length, the answer is x=12.85ft