A 40 cm wire is cut into two pieces, and each piece is bent into a square. What is the smallest possible total area of the two squares?
Answer and explanation
Correct answer: B. , when the wire is cut in half
- Step 1: If one piece has length , the sides are and , so the area is . Step 2. The derivative is zero at , and the area is . **Answer: , when the wire is cut in half. Why not the others:** is the area of one square made from the whole wire, is the area of just one of the two equal squares, and a piece of 10 cm gives a larger total of .
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