SOLUTION: A wire L = 16 cm long is cut into two pieces, one of length x and the other of length (L - x). Each piece is bent into the shape of a square.
(a) Find a function that models the
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(a) Find a function that models the
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Question 404474: A wire L = 16 cm long is cut into two pieces, one of length x and the other of length (L - x). Each piece is bent into the shape of a square.
(a) Find a function that models the total area A enclosed by the two squares in terms of x.
A(x) =
(b) Find the value of x that minimizes the total area of the two squares.
x = ____ cm Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website! Since the perimeters of the two squares are x and L-x respectively, then the side lengths are and . The sums of the two areas are:
The minimum occurs when is minimized, which also happens when is minimized. Either using the vertex of the parabola or by differentiating, we obtain , so the minimum area occurs when the wire is cut into two pieces of 8 cm.
