Question 229970: A wire 10 cm long is cut into 2 pieces, one of length x and the other of length 10-x. Each piece is bent into the shape of a square.
a) Find a function that models the total area enclosed by the two squares.
Would the function be A(x)=-(x+5)²+25?
b) Find the value of x that minimizes the total area of two squares.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A wire 10 cm long is cut into 2 pieces, one of length x and the other of length 10-x. Each piece is bent into the shape of a square.
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If total length is "x", each side of the square is x/4
and the area is (x/4)^2
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If total length is "10-x", each side of the square is (10-x)/4
and the area is [(10-x)/4]^2
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a) Find a function that models the total area enclosed by the two squares.
Total Area = (x/4)^2 + [(10-x)/4]^2
TA = (x^2/16) + [(100 -20x + x^2)/16]
TA = (1/8)x^2 -(5/4)x + (25/4)
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b) Find the value of x that minimizes the total area of two squares.
Min occurs when x = -b/2a = (5/4)/[2(1/8)] = (5/4)/(1/4) = 5
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Cheers,
Stan H.
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