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Calculus/Maximum-minimum problem

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Expert: - 12/7/2009


Question
Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle with sides of length 20 if one side of the rectangle lies on the base of the triangle.  

Answer

Rectangle
Questioner: Prae
Question: Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle with sides of length 20 if one side of the rectangle lies on the base of the triangle.

In the picture,


A = 2xy, to be maxed.

y = (10-x) sin 60 = (10-x) sqrt(3)/2

A = 2x((10-x) sqrt(3)/2

A = x((10-x) sqrt(3)

Take it from there.  

Paul Klarreich

Expertise

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

Experience

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

Education/Credentials
(See above.)

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