A Piece of Wire $14 \mathrm {~m}$ Long Is Cut into Two Pieces

question 22

Multiple Choice

A piece of wire $14 \mathrm {~m}$ long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum?
Round your answer to the nearest hundredth. Select the correct answer.

• A) \(0 \mathrm {~m}\)
• B) \(6.09 \mathrm {~m}\)
• C) \(8.09 \mathrm {~m}\)
• D) \(10.09 \mathrm {~m}\)
• E) \(9.09 \mathrm {~m}\)

---

Definitions:

Transaction Costs

Expenses incurred when buying or selling goods and services, which may include search and information costs, bargaining costs, and enforcement costs.

Voluntary Exchange

A transaction where parties involved trade goods or services by mutual agreement, without coercion.

Mutual Gain

A situation or outcome in which all parties involved benefit or profit from the arrangement or transaction.

Potential Exchange

The possibility of trading goods, services, or other items of value between parties.