Friday, June 12, 2015

College Algebra, Chapter 4, 4.1, Section 4.1, Problem 74

Suppose that a wire 10 cm long is cut into two pieces, one of length x and the other of length 10x. Each piece is bent into the shape of a square.

a.) Find a function that models the total area enclosed by the two squares.

b.) Find the value of x that minimizes the total area of the two squares.

a.) If A1=x2 be the area of the square with length x, then A2=(10x)2 is the area of the other square. Thus, the total area is AT=A1+A2.


AT=x2+(10x)2AT=x2+10020x+x2AT=2x220x+100


b.) The function AT is a quadratic function with a=2 and b=20, thus, its minimum value occurs when

x=b2a=(20)2(2)=204=5 cm

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