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
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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(52778) (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
---------------------
Formula for area of a rectangle:
-------------------------
The formula for is
------------------------------
Plug this result back into equation
This shows that the maximum area is a square
( which is always true )
-------------------------
Here's the plot od
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