The Vsum of the Perimeters of an Equilateral Triangle and a Square

question 120

Multiple Choice

The vsum of the perimeters of an equilateral triangle and a square is 19. Find the dimensions of the triangle and the square that produce a minimum total area.

• A)side of square: \(\frac { 19 } { 4 + 9 \sqrt { 3 } }\); side of triangle: \(\frac { 57 \sqrt { 3 } } { 4 + 9 \sqrt { 3 } }\)
• B) side of square: \(\frac { 19 \sqrt { 3 } } { 9 + 4 \sqrt { 3 } }\); side of triangle: \(\frac { 57 } { 9 + 4 \sqrt { 3 } }\)
• C) side of square: \(\frac { 57 \sqrt { 3 } } { 4 + 9 \sqrt { 3 } }\); side of triangle: \(\frac { 19 } { 4 + 9 \sqrt { 3 } }\)
• D) side of square: \(\frac { 19 } { 9 + 4 \sqrt { 3 } }\); side of triangle: \(\frac { 38 \sqrt { 3 } } { 9 + 4 \sqrt { 3 } }\)
• E) side of square: \(\frac { 57 } { 9 + 4 \sqrt { 3 } }\); side of triangle: \(\frac { 19 } { 9 + 4 \sqrt { 3 } }\)

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Definitions:

Double-Markup Problem

A situation in vertical supply chains wherein two or more successive stages (like wholesalers and retailers) mark up the prices of goods, potentially leading to excessively high retail prices.

Vertical Relationships

The interactions and connections between different levels of a supply chain, such as manufacturers and distributors.

Profits

The financial gain obtained when the total revenue generated from business activities exceeds the total costs and expenses incurred.

Arbitraging

The practice of taking advantage of a price difference between two or more markets by buying low in one and selling high in another.