SOLUTION: An architect is designing an atrium for a hotel. The atrium is to be rectangular with a perimeter of 688 ft of brass piping. What dimensions will maximize the area of the&#8203; at

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Question 1058527: An architect is designing an atrium for a hotel. The atrium is to be rectangular with a perimeter of 688 ft of brass piping. What dimensions will maximize the area of the atrium?
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.
A rectangle with the given perimeter which has maximal area is a SQUARE.

To find the side length of the square divide 688 ft by 4: side = = 172 ft.

See the lesson
    - A rectangle with a given perimeter which has the maximal area is a square
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".

The other lessons under this topic are
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
    - A farmer planning to fence a rectangular garden to enclose the maximal area
    - A farmer planning to fence a rectangular area along the river to enclose the maximal area
    - A rancher planning to fence two adjacent rectangular corrals to enclose the maximal area

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
Formula for perimeter of rectangle:

ft

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Formula for area of a rectangle:

-------------------------
The formula for is

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Plug this result back into equation

This shows that the maximum area is a square
( which is always true )
-------------------------
Here's the plot od

SOLUTION: An architect is designing an atrium for a hotel. The atrium is to be rectangular with a perimeter of 688 ft of brass piping. What dimensions will maximize the area of the&#8203; at

SOLUTION: An architect is designing an atrium for a hotel. The atrium is to be rectangular with a perimeter of 688 ft of brass piping. What dimensions will maximize the area of the at